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Author Index
Aavatsmark, I., 322Abeyaratne, R., 267Agemi, R., 143Airy, G.B., XIX, 227, 228Alber, H.D., 474, 513Albeverio, S., 321Alekseyevskaya, T.V., 227Alinhac, S., 95, 228Amadori, D., 227, 269, 372, 474, 475, 515,
569Ambrosio, L., 24, 194, 370Amorim, P., 192Amundson, N.R., 226, 227Ancona, F., 321, 372, 474, 513–515, 542Andreianov, B.P., 192Andrianov, N., 324Antman, S.S., 50, 73, 227, 266Anzellotti, G., 23Aris, R., 226, 227Arun, K.R., 74Asakura, F., 267, 475Audusse, E., 192Avelaneda, M., 372Aw, A., 226Ayad, S., 432Azevedo, A.V., 323
Backer, M., 193Bae, M.-j., 595Bagnerini, 226, 568Baiti, P., 269, 324, 372, 513–515, 542Bakhvarov, N., 474Ball, J.M., 50, 144, 568
Ballmann, J., 73Ballou, D., 372Bang, Seunghoon, 595Bardos, C., 96, 193Barker, B., 269Barker, L.M., 512Barnes, A.P., 475Bascar, S., 323Bateman, H., XXIX, 95Baudin, M., 142Bauman, P., 194Beale, T., 95Becker, R., XXVII, 266Bedjaoui, N., 142, 267Ben Moussa, Bachir, 568Ben-Artzi, M., 192, 324Ben-Dor, G., 595Benabdallah, A., 144Benilan, Ph., 192, 372Benzoni-Gavage, S., 72, 73, 141, 142, 144,
226, 267–269, 371, 570Bereux, F., 570Bernoulli, D., XVIBers, L., 594Berthelin, F., 73, 142, 226, 570Bertoin, J., 372Bertozzi, A.L., 266Bethe, H.A., XXVII, 265, 266Bethuel, F., 321Bianchini, S., 142, 321, 323, 513, 514, 542Blaser, M., 322Bloom, F., 73Boillat, G., 24, 73, 143, 228
694 Author Index
Bolley, F., 193Bonnefille, M., 571Bonnetier, E., 570Born, M., 73Botchorishvilli, R., 193Bouchut, F., 142, 193, 194, 371, 570Bourdarias, C., 226Boyle, R., XVBrenier, Y., 144, 193, 321, 371Brenner, P., 194Bressan, A., 72, 194, 229, 323, 474,
512–515, 542Brio, M., 267Burger, R., 194, 227, 228Burgers, J., XXVIII, XXIXBurton, C.V., XXVI
Cabannes, H., 73Caflisch, R.E., 266Caginalp, G., 192Canic, S., 267, 323, 595, 596Carasso, C., 73Caravenna, L., 475Carrillo, J.A., 194, 370Cauchy, A.-L., XVI, 23, 50Cercignani, C., 73, 142Chae, Dongho, 143Challis, J., XVII, 95Chalons, C., 323Chang, Tung, 72, 265, 266, 320, 321, 594,
596Chaplygin, S.A., 51Chasseigne, E., 372Chemin, J.-Y., 141, 142, 228Chen, Gui-Qiang, 23, 72, 74, 96, 142, 143,
193, 194, 321, 372, 475, 514, 542,568–571, 594–596
Chen, Jing, 73Chen, Jun, 143, 595Chen, Peter J., 228Chen, Shuxin, 324, 594, 596Cheng, Kuo-Shung, 372Cheret, R., XVChern, I-Liang., 268Cheverry, C., 372, 474, 571Choksi, R., 227, 371Choquet-Bruhat, V., 571Chorin, A.J., 73Christodoulou, D., 73, 95, 143
Christoffel, E.B., XXII, 24Christoforou, C.C., 514, 542Chueh, K.N., 569Ciarlet, P.G., 49, 50Clausius, R., XXIII, 50Cockburn, B., 193Coclite, G.M., 194, 226, 372, 514, 515, 568Cole, J.D., XXIXColeman, B.D., 50, 51, 73Collet, J.F., 569Colombo, R.M., 226, 372, 513–515Conley, C.C., 266, 569Conlon, J.G., 227, 228, 266, 372Conway, E.D., 192, 194Coquel, F., 142, 193, 194, 323, 568, 569Corli, A., 228, 268, 298, 323, 475, 512, 513,
515Correia, J., 321Corrias, L., 371Cosserat, E., 51Cosserat, F., 51Costanzino, N., 269Coulombel, J.-F., 268Courant, R., XXVIII, 72, 192, 265, 320, 324,
432, 594Crandall, M.G., 192, 193, 372Crasta, G., 513, 515Crippa, G., 193Currie, J.C., 50
D’Apice, C., 226Dacorogna, B., 144Dafermos, C.M., 50, 72, 143, 144, 194, 227,
266, 321, 322, 330, 370–372, 432,433, 475, 512, 514, 569, 570
Dalibard, A.-L., 193DalMaso, G., 269Danilov, V.G., 228, 321De Lellis, C., 96, 193, 194, 370, 371De Morgan, A., XXDegiovanni, M., 23Degond, P., 226Delitala, P., 226Demengel, F., 568DeMottoni, P., 323Demoulini, S., 50, 95, 144, 569Despres, B., 322DeVore, R.A., 193Dias, J.P., 371
Author Index 695
Diehl, S., 372DiFrancesco, M., 142, 370Dill, E.H., 73Ding, Xia Xi, 371, 372, 569Ding, Yi, 372DiPerna, R.J., 24, 143, 193, 322, 432, 474,
513, 514, 567–569, 571Donadello, C., 515, 542Donatelli, D., 142Donato, A., 73Douglis, A., 192, 228Dressel, A., 266Dressler, K., 193Du, Qiang, 193DuBois, F., 96Dubroca, B., 475Duhem, P., XXIV–XXVI, 50
E, Weinan, 194, 372Earnshaw, S., XX, 51, 227, 228Ehrt, J., 371Elling, V., 595Engelberg, S., 143Engquist, B., 72, 73, 194Ercole, G., 321–323Ericksen, J.L., 50Erpenbeck, J., 268Euler, L., XI, XVI, 24, 50Evans, L.C., 24, 72, 567Even, N., 372
Falcovitz, J., 192Fan, Haitao, 142, 267, 322, 323, 371Fang, Beixiang, 595Federer, H., 24Feireisl, E., 143, 194Feldman, M., 143, 595, 596Ferrari, C., 594Ferziger, J.H., 321Fey, M., 73Fife, P.C., 227Filippov, A.F., 330Fonseca, I., 144Foy, R.L., 266Francheteau, J., 268Freistuhler, H., 73, 194, 227, 267, 268, 323Frid, H., 23, 143, 194, 323, 475, 514, 568,
570
Friedrichs, K.O., XXVIII, 24, 72, 73, 142,228, 320, 324, 432, 594
Fries, C., 268Fusco, D., 432Fusco, N., 24
Garding, L., 142Gallavotti, G., 50Gallice, G., 475Gangbo, W., 96Garavello, M., 226, 372Gardner, R.A., 269Gariepy, R.F., 24Gay-Lussac, J.L., XVGelfand, I., 266, 321, 575Geng, Xiao, 227, 432, 433, 514Geng, Zhenwen, 595Gerbeau, J.-F., 227Gibbs, J.W., XXIIIGiga, Y., 193Gilbarg, D., XXVIII, 266Gimse, T., 512Gisclon, M., 144, 226Giusti, E., 24Glass, O., 513, 543Glimm, J., 73, 323, 324, 330, 432, 433, 474,
514, 570, 595Goatin, P., 226, 321, 371, 372, 513–515, 575Godin, P., 268Godlewski, E., 72, 193, 320Godunov, S.K., 24, 142, 228Godvik, M., 226Golse, F., 193Goodman, J., 267, 268, 542Gosse, L., 372, 475, 514, 515, 569Graham, M.J., 73Grassin, M., 95Greenberg, J.M., 226, 324, 372, 569Grenier, E., 144, 371, 372Greven, A., 73Gripenberg, G., 569Groah, J., 73, 324Grot, R.A., 73Grove, J.W., 73Guckenheimer, J., 372, 594Guerra, G., 372, 474, 475, 514, 515, 569Gues, O., 144, 228, 269Guo, Yan, 143Gurtin, M.E., 23, 49–51
696 Author Index
Gustafsson, B., 73Gwiazda, P., 226
Ha, Seung-Yeal, 143, 475Ha, Youngsoo, 372Hadamard, J., XXIVHagan, R., 267Hale, J.K., 371Hamel, G., 23Hanche-Olsen, 226, 323Hanouzet, B., 142, 569Hanyga, A., 49Harten, A., 73Harterich, J., 142, 371Hartman, P., 228Hattori, H., 322, 323Hayes, B.T., 267, 269, 321, 372Hayes, W.D., 594He, Cheng, 143Hedstrom, G.W., 512Heibig, A., 228, 322, 432, 433, 514, 570,
571, 595Heidrich, A., 569Herty, M., 226Higdon, R.L., 144Hilbert, D., 192Høegh-Krohn, R., 512Hoff, D., 269, 371, 474, 542, 569Holden, H., 72, 226, 227, 321, 323, 372,
474, 512, 515Holden, L., 512Holder, E., XIIHong, John, 321, 475Hopf, E., XXVIII, 192, 370Hormander, L., 72, 228, 330, 567Hou, Thomas, 73Howard, P., 269Hrusa, W.J., 143, 144Hsiao, Ling, 72, 96, 142, 265, 266, 268, 320,
323, 475, 594Hu, Jiaxin, 513Hua, Jiale, 474Huang, Feimin, 143, 268, 321, 371, 372,
570, 596Hughes, T.J.R., 50, 144Hugoniot, H., XXIII, XXIV, XXVI, 265Huh, Hyungjin, 143Humpherys, J., 269Hunter, J.K., 267, 571
Hwang, Seok, 193, 568
Igutsi, Tatsuo, 321, 324, 474Ilin, A.M., 267Infeld, L., 73Isaacson, E.L., 194, 323, 372, 475Izumiya, S., 192
Jacobs, D., 267James, F., 193, 371James, R.D., 267Janenko, N.N., 72Jang, Juhi, 95, 143Jeffrey, A., 72, 73, 324Jegdic, K., 595Jeltsch, R., 73Jenssen, H.K., 227, 269, 324, 372, 513, 542Ji, Xiaomei, 595Jiang, Guang-Shan, 269Jiang, Song., 96, 542Jiang, Zaihong, 474Jin, Shi, 142, 193, 371, 569John, F., 95, 228Johnson, J.N., XVJoly, J.-L., 324, 571Joseph, K.T., 144, 321, 322Jouguet, XXIV, XXV, 95Junca, S., 142, 226, 571
Kalasnikov, A.S., 322Kan, Pui-Tak, 570Kaper, H.G., 321Karlsen, 194, 512, 515, 568Kato, T., 95, 141, 142, 144Katsoulakis, M.A., 193Kawashima, S., 96, 142, 268Keller, G., 73Keller, J.B., 571Kelvin, Lord, XVIII, XXIIKeyfitz, B.L., 227, 267, 321–323, 595, 596Khanin, K., 372Kim, Eun Heui, 595Kim, Jong Uhn, 372Kim, Yong Jung, 321, 370, 371Kirchhoff, G., XXIII, 50Klainerman, S., 143, 228Klar, A., 226Klausen, R.A., 372Klingenberg, C., 142, 372, 475, 569
Author Index 697
Knowles, J.K., 267Kogan, I.A., 227Kohler, M., 321Kondo, C.I., 194, 568Kong, De-Xing, 324Kossioris, G.T., 192Kranzer, H.C., 227, 321–323Krehl, P., XXIIKreiss, G., 144, 269Kreiss, H.O., 144, 269Krejci, P., 322Kroner, D., 72, 193Kruger, L.H., 51, 72Kruzkov, S., 95, 149, 192Kulikovski, A.G., 72, 73Kuznetsov, N., 192Kwon, Young-Sam., 193, 194
Lagrange, J.L., 227Lan, Chiu-Ya, 475Landau, L.D., 73, 571Laplace, P.S., XVI, XVIILattanzio, C., 142–144, 268, 370, 371, 542,
569, 570Lax, P.D., XXX, 23, 24, 72, 73, 95, 142,
226–228, 265, 266, 320, 330, 370,432, 433, 474, 514, 575
Lee, Young Ran, 372LeFloch, P.G., 72, 96, 142, 144, 192–194,
267, 269, 321–324, 371, 474, 475,513–515, 542, 543, 568, 570
Legendre, A.M., XVIILei, Zhen, 595Leibovich, L., 321Leroux, A.-Y., 96, 193LeVeque, R.J., 72, 193, 433Levermore, C.D., 73, 142, 569Lewicka, M., 229, 268, 514, 515Li, Bang-He, 569, 570Li, Cai Zhong, 474, 475, 514Li, Dening, 594, 595Li, Hailiang, 143, 542Li, Jiequan, 72, 321–324, 372, 594–596Li, Ta-Tsien, 143, 228, 265, 324Li, Tian-Hong, 324, 569, 570, 595Li, Tong, 226Li, Xiaolin, 595Li, Yachun, 143, 514Lieberman, G.M., 595
Lien, Wen-Ching, 475, 595Lifshitz, E.M., 73Liggett, T.M., 192Lighthill, M.J., 226, 571Lin, Huey-Er, 475Lin, Long-Wei, 323, 474, 475, 512, 513, 542Lin, Peixiong, 569Lin, Xiao-Biao, 269, 322Lindquist, W.B., 594Lions, P.-L., 143, 193, 370, 569–571Liu, Hailiang, 143, 226, 268, 321, 322Liu, Hongxia, 371Liu, I-Shih, 323Liu, Jian Guo, 73, 227, 269Liu, Tai-Ping, 72, 95, 142–144, 194, 227,
228, 266–269, 321, 324, 371, 372,432, 433, 474, 475, 513, 514, 542,568, 569, 595
Liu, Weishi, 323Loeper, G., 193Lorenz, J., 269Lu, Yun-Guang, 72, 568–570Lucier, B.J., 193, 371, 515Luo, Pei Zhu, 569Luo, Tao, 142, 143, 324, 475, 569, 570Luskin, M., 474, 475Lyberopoulos, A.N., 371Lyng, G., 269Lyons, W.K., 372Lyubimov, A., 73
MacCamy, R.C., 143Mach, E., XXII, 595MacKinney, W., 267Mailybaev, A.A., 266, 267Majda, A., 72, 95, 142, 192, 193, 227, 228,
266, 268, 571Makino, T., 142Malek, J., 194, 567, 568Malek-Madani, R., 266Mallet-Paret, J., 323Manzo, R., 226Marcati, P., 142, 371, 569, 570Marchesin, D., 266, 267, 322, 323Marigo, A., 226Mariotte, E, XVMarkowich, P., 143Marsden, J.E., 50, 73, 144Marson, A., 321, 372, 474, 513–515
698 Author Index
Martins, C., 23Marzocchi, A., 23Mascia, C., 268, 269, 371, 372Masmoudi, N., 95Matano, H., 371Matsumura, A., 268Mauri, C., 226Maxwell, J.C., 51Mazel, A., 372Mei, Ming, 143Menon, G., 372Mercier, J.M., 323Metivier, G., 142, 144, 268, 269, 324, 571Min, Jianzhong, 595Mitrovic, H.D., 228Miyakawa, T., 193Mizel, V.J., 50Mock, 266Morawetz, 570, 594Morokoff, W.J., 73Morrey, C.B., 144Muller, I., 49, 50, 73, 227Muller, S., 144Murat, F., 143, 269, 567, 568Musesti, A., 23
Natalini, R., 142–144, 192, 193, 268, 372,568–570
Necas, J., 193, 567Nedelec, J.-C., 96, 194, 371Nessyahu, H., 371Neves, W., 144, 229Ni, Guoxi, 542Nickel, K., 370Nicolaenko, B., 266Nishibata, 142, 268Nishida, T., 474, 475Nishihara, K., 143, 268Noelle, S., 193, 324Nohel, 143Noll, W., 23, 49, 50, 73Nouri, A., 194
Oh, Myunghyun, 269Oleinik, O.A., 266, 267, 370, 514Oliveri, F., 73Olver, P.J., 50Omrane, A., 194Osher, S., 371
Ostrov, D.N., 323, 372, 433Otto, F., 192, 193, 371, 568
Paes-Leme, P., 323Pallara, D., 24Pan, R., 142, 268, 512, 542, 570Panov, E. Yu., 192–194, 321, 371, 568Pant, V., 73Park, Rea, 542Pego, R.L., 266, 267, 372, 475, 571Pence, T.J., 267, 322, 323Peng, Yue-Jun, 50, 193Perepelitsa, M., 475Pericak-Spector, K.A., 324Perthame, B., 72, 192, 193, 227, 268,
569–571Peters, G.R., 323Petzeltova, H., 194Philips, D., 193, 194Piccoli, B., 226, 269, 323, 372, 513, 515Pierre, M., 372Plaza, R., 268, 269Plohr, B.J., 73, 267, 322, 323Pogorelov, N.V., 72Poisson, S.D., XVI, 50, 228Portilheiro, M., 192, 193Poupaud, F., 143, 330, 568Prasad, P., 74, 323Priuli, F.S., 226Probstein, R.F., 594Pulvirenti, M., 193
Qin, Tiehu, 50, 144Quinn, B., 371
Racke, R., 143Raizer, Yu., 72Rankine, W.J.M., XVI, XXII, XXIIIRaoofi, M., 269Rascle, M., 142, 143, 193, 226, 330, 568,
569, 571Rauch, J., 194, 324, 571Raviart, P.-A., 72, 73, 193, 194, 320Rayleigh, Lord, XVIII, XXIII, XXVI,
XXVII, 96, 266Renardy, M., 143Rezakhanlou, F., 371Rhee, Hyun-Ku, 226, 227
Author Index 699
Riemann, B., XX, 95, 227, 265, 320, 432,575
Ringhofer, C.A., 143Risebro, N.H., 226, 321, 323, 372, 474, 475,
513, 515Riviere, T., 193, 322Rivlin, R.S., 50Robyr, R., 372Rohde, C., 142, 143, 322Rokyta, M., 194, 567Rosakis, P., 267Rosales, R.R., 571Rousset, F., 144, 542Roytburd, V., 568Rozdestvenskii, B.L., 72, 192Rubino, B., 143, 569, 570Rudd, K., 269Ruggeri, T., 24, 73, 142, 227, 266Ruzicka, M., 194, 567Rykov, Yu., 371Ryzhik, L., 268
Sable-Tougeron, M., 268, 475Sahel, A., 433Saint-Venant, A.J.C., 227Sande, H., 474, 515Sanders, R., 595Santos, M.M., 570Saxton, K., 143Schaeffer, D., 267, 323, 370, 595Schatzman, M., 514Schauder, J., XXVIII, 142Schecter, S., 267, 322, 323Schmeiser, C., 143Schmidt, B.G., 475Schochet, S., 371, 474, 475, 513, 514, 568,
571Schonbek, M.E., 568, 571Schulz-Rinne, C.W., 596Schulze, S., 267, 323Semenov, Yu., 72Serre, D., 72, 73, 95, 96, 141–144, 226–229,
265–269, 320–322, 324, 371, 372,433, 474, 475, 542, 568–571, 595
Sevennec, B., 227Sever, M., 228, 321, 322, 372Shandarin, S.F., 227Shearer, J.W., 569Shearer, M., 266, 267, 323, 324, 371, 372
Shelkovich, V.M., 321Shelukhin, V., 570Shen, Wen, 142, 227–229, 542Sheng, Wancheng, 321, 322Shiffman, M., 594Shizuta, Y., 96Sideris, T., 95, 143Silhavy, M., 23, 49, 50Simic, S., 227Sinai, Ya. G., 371, 372Sinestrari, C., 192, 371, 372Slemrod, M., 74, 96, 143, 267, 322, 323,
568, 570Smets, D., 322Smith, R.G., 321Smoller, J.A., 72, 73, 143, 192, 226, 265,
266, 320, 321, 324, 370, 474, 475, 569Sod, G.A., 72Song, Kyungwoo, 595Souganidis, P.E., 570Spector, S.J., 324Spinolo, L.V., 323, 542Stewart, J.M., 475Stoker, J.J., 227Stokes, G.G., XVII, XIX, XXVI, 24, 95, 228Straskraba, I., 322Strauss, W., 143Strumia, A., 24Stuart, D.M.A., 50, 96, 144, 569Sun, Wenjun, 542Sverak, V., 144Szekelyhidi, 96Szeliga, W., 324Szepessy, A., 193, 194, 268, 568Szmolyan, P., 267, 322
Tadmor, E., 72, 73, 142, 143, 193, 322, 371,372, 568, 569
Tan, De Chun., 321–323, 594, 596Tang, Tao, 142, 372, 542Tang, Zhi Jing, 323Tao, Terence, 193Tartar, L.C., 72, 143, 567, 568Taub, A.H., 73Taylor, G.I., XXVII, 96, 266Taylor, M.E., 72, 142, 567Temple, B., 73, 194, 265, 321, 323, 324,
372, 432, 433, 474, 475, 513Teng, Zhen-Huan, 371, 542
700 Author Index
Terracina, A., 142, 372Tesdall, A.M., 595Tesei, A., 192, 569Texier, B., 269Thanh, M.D., 267, 321, 323, 324Tidriri, M., 194Ting, T.C.T., 323Tong, Donald D.M., 372Toro, E., 72Torres, M., 23Toupin, R.A., 49, 50Towers, J.D., 515Tran, H., 142Tricomi, F., 594Trivisa, K., 432, 514, 515Truesdell, C.A., XV, XVI, 49, 50, 73Truskinovsky, L., 267Tsarev, S.P., 228Tsikkou, C., 324, 432Tsuge, N., 570Tupciev, V.A., 322Tveito, A., 142, 194, 228, 512, 513, 569Tzavaras, A.E., 50, 73, 96, 142–144, 193,
269, 322, 323, 370, 568–571
Ueda, Y., 268Ukai, S., 142
van der Geest, M., XXIIvan der Waals, J.D., 50Vasseur, A., 73, 193, 570Vecchi, I., 568Venttsel’, T.D., 569Vila, J.P., 143, 194Villani, 73, 96Vincenti, W.G., 51, 72Volpert, A.I., 24, 192von Karman, T., XXVIIIvon Mises, R.V., XXIV, 51, 432, 594von Neumann, J., XXVIII, 595
Wagner, D.H., 50, 475, 594Wang, Chao Chen, 50Wang, Ching-Hua, 194, 372, 474Wang, Dehua, 72, 74, 143, 324, 475, 570,
595Wang, Kenji, 143Wang, Libin, 228, 324Wang, Wei-Cheng, 142
Wang, Ya-Guang, 596Wang, Yi, 268Wang, Zejun, 475, 570Wang, Zhen, 371, 372, 570Warnecke, G., 73, 267, 324, 372Weber, H., XXIV, XXVI, 95Wei, Dongming, 143Weinberger, H., 372Wendland, W.L., 227Wendroff, B., 266, 321, 513Westdickenberg, M., 96, 193, 371, 568, 570Weyl, H., XXVIII, 265, 266Whitham, G.B., 72, 226, 227, 568, 571Williams, M., 144, 227, 269Winter, A., 228Winther, R., 142, 194, 569Wu, Zhuo-Qun, 330
Xiao, Ling, 143, 570Xie, Chungjing, 595Xin, Zhou Ping, 142, 144, 193, 228, 265,
268, 269, 514, 542, 569, 570, 595Xu, Xiangsheng, 142, 372Xu, Zhengfu, 542
Yan, Baisheng., 324Yang, Hanchun, 321, 322Yang, Shuli., 72, 321, 594, 596Yang, Tong, 95, 142, 143, 228, 266, 268,
321, 323, 324, 371, 474, 475, 513,514, 542, 568–570, 594
Yang, Xiaozhou, 595, 596Yang, Yadong, 323Ye, Xiao Ping, 474Yi, Zhou, 228Yin, Huicheng., 595Ying, Lung An, 474Yong, Wen-An, 142–144, 266, 324Yongqian Zhang, 595Young, L.C., 568Young, R., 324, 433, 474Yu, Shih-Hsien, 142, 266, 268, 269, 542Yu, Wen-Ci, 228, 265Yuan, Hairong, 595
Zeldovich, Ya. B., 72, 227Zemplen, G., XXVZeng, Wang, 268Zhang, Mei, 266
Author Index 701
Zhang, Peng, 322, 324, 594–596Zhang, Tong, 72, 266, 267, 321–324,
594–596Zhang, Yonqian, 514, 595, 596Zhao, Huijiang, 142, 268, 568, 570Zhao, Yinchuan, 372Zheng, Songmu, 96
Zheng, Yuxi, 72, 321–324, 594–596
Zhu, Changjiang, 95, 142, 266, 268, 568
Zhu, Dianwen, 595, 596
Zhu, Guangshan, 323
Ziemer, W.P., 23
Zumbrun, K., 144, 266, 268, 269, 323, 433
Subject Index
acoustic tensor, 57, 199adiabatic exponent, XVI, 40adiabatic flow, XVIadiabatic process, 42admissibility criteria for weak solutions
entropy, ff .83entropy rate, ff .290entropy shock, ff .248entropy, for measure-valued solutions,
549Lax shock, ff .240Liu shock, ff .246vanishing viscosity, ff .87viscosity-capillarity, 91viscous shock, ff .252
admissibleshocks, ff .231wave fans, ff .274
approximatecharacteristic, 446conservation law, 446Riemann solver, ff .482solution, ff .486
balance laws, ff .1angular momentum, 32companion, ff .13, ff .22energy, 33entropy, 33homogeneous, 12in Continuum Physics, ff .28inhomogeneous system of, ff .463linear momentum, 32
mass, 31, 32of continuum thermomechanics, ff .31scalar, 12, 56symmetric, 14symmetrizable, 14system of, ff .12
barotropic flow, XVI, 65Bernoulli equation, XVI, 65binary mixture, 202body, 25body force, 32Boltzmann equation, 65Born-Infeld constitutive relations, 69Boyle’s law, 40breakdown
in scalar conservation law, ff .146of classical solutions, ff .78, 221of weak solutions, ff .317
Buckley-Leverett equation, 196Burgers equation, XXIX, 78, 88, 218BV functions, ff .17
bounded variation, 17irregular point of, 18locally bounded variation, 17normalized composition of, 18point of approximate continuity of, 18point of approximate jump discontinuity
of, 18special, 20, 273, 338total variation of, 17trace, inward or outward, of, 19
BV solutions, ff .21, ff .325
704 Subject Index
caloric equations, XXIII, 42Cauchy problem, ff .75Cauchy stress, 32Cauchy tetrahedron argument, 5Chaplygin gas, XX, 41, 595Chapman-Enskog expansion, 142characteristic
approximate, ff .444classical, 146, 204generalized, ff .325in front tracking scheme, 486
characteristic speed, 54, 204characteristic tree, ff .400chromatography, 227Clausius-Duhem inequality, 32, 33combustion, ff .202compactness and consistency
of front tracking algorithm, ff .494of random choice algorithm, ff .438
companion balance law, ff .13, ff .22compensated compactness, ff .545conservation law
approximate, 446canonical form of, 54system of, 12
constant state, 217constitutive equations, 12
of thermoelasticity, ff .36of thermoviscoelasticity, ff .44
contact discontinuity, 242continuity equation, 32, 69continuum physics, ff .25continuum thermomechanics, ff .31contraction semigroup, ff .158Crandall-Liggett theory, 163
damping, ff .108deformation gradient, 27density, 32density flux function, 2diffusion wave, 261, 262dissipation inequality, 34div-curl lemma, ff .547divide, 329, ff .340, 348, 430duct of varying cross section, 201, 466
E-conditionLax, ff .240, 242, 247, 250, 251, 259, 276,
283, 325, 332
Liu, ff .246, 247, 249, 251, 257, 274, 283,287
Oleinik, 247, 249, 257, 283, 292Wendroff, 248, 250, 257, 260, 283, 292
elastic string, 199, 200electrodynamics, ff .68electromagnetic field energy, 69, 71electromagnetic waves, 201, 210electrophoresis, 209, 215entropy, XXIII, 33, ff .54, ff .211
admissibility criterion, ff .83, 550contingent, ff .129flux, 33, 55Kruzkov, 149Lax, 376physical, 33production across shock, 248production measure, 84rate admissibility criterion, 87, ff .290relative, 119shock admissibility criterion, ff .248weak, 565
entropy-entropy flux pairs, 211equidistributed sequence, 440, 462Euler’s equations, XVI, 73, 86Euler-Poisson system, 113Eulerian formulation (coordinates), 26explosion of weak fronts, ff .220extended thermodynamics, ff .65, 67extensive quantity, 2
fading memory, 117field equation, ff .3fine structure, ff .180finite perimenter, set of, 19
measure theoretic boundary of, 19reduced boundary of, 19
flow past a ramp of gentle slope, ff .583Fourier law, 40front
rarefaction, 481shock, 15weak, 15
front tracking method, ff .477for scalar conservation laws, ff .478for systems of conservation laws, ff .480
generalized characteristics, ff .325extremal backward, ff .327
Subject Index 705
for scalar balance laws, 359for scalar conservation laws, ff .332for systems of two conservation laws, ff
.378left contact, 328maximal, 327minimal, 327right contact, 328shock free, 328, 359
generation order of wave, 485genuine nonlinearity, 214, 219, 221, 224,
236, 239, 243, 247, 251, ff .278, 310,329, ff .331, ff .373, ff .444, ff .448, ff.453, ff .455, ff .481, ff .556
geometric optics, 571Gibbs relation, XIII, 39Glimm functional, ff .448
continuous, ff .507Godunov’s scheme, 542, 559, 564gravity waves, 200
Hamilton-Jacobi equation, 344heat flux, 33heat supply, 33Helly’s theorem, 20Helmholtz free energy, 41hodograph transformation, XXI, 377Hopf-Cole transformation, XXIXHugoniot equation, XXIV, 233Hugoniot locus, XXII, ff .234hydrodynamic model of semiconductors,
114hydrostatic pressure, 40, 47hyperbolic systems, ff .53hyperelasticity, 42
ideal polytropic gas, XXIII, 40incompressibility, ff .47inhomogeneous systems of balance laws, ff
.463initial-boundary value problem, ff .91, ff
.138, ff .184interaction of wave fans, ff .309internal energy, XXIII, 33internal state variable, 48invariants for scalar conservation laws, ff
.340involution, ff .119involution cone, 120
irreversibility, 83irrotational flow, 65, 129, 579, ff .580, 585,
ff .588, ff .591isentropic
flow, XVIgas dynamics, 198, ff .564process, 42steady gas flow, ff .576(thermo) elasticity, 43, ff .59, 198, 233,
243, 247, 249, 257, 279, 283, 374, ff.559
isochoric, 29isothermal flow, XVIisothermal process, 42isotropic thermoelastic solid, 41
jump condition; see also “Rankine-Hugoniotjump condition”, 16
Kawashima condition, 89, 96, 110Kawashima-Shizuta condition, 96kinematic conservation laws, 58kinetic formulation, ff .174kinetic relation, 242, 264Kreiss-Lopatinski condition, 139
Lagrangian formulation (coordinates), 26lap number, 351, 479Lax
entropies, 376, 557formula, 340shock admissibility criterion, ff .240
Lax E-condition, XXII, 242Lax-Friedrichs scheme, 192, 438, 542, 559,
564layering method, ff .164Legendre-Hadamard condition, 57linear degeneracy, 214, 238, 250, 278, 279,
481, 570linearly nondegenerate, 181Liu
shock admissibility criterion, ff .246
Mach reflection, XXII, 591Mach stem, 591magnetohydrodynamics, ff .71mass explosion, 79material frame indifference, ff .35, 38, 45, 59material symmetry, 39, 46Maxwell stress tensor, 71
706 Subject Index
Maxwell’s equations, ff .68measure-valued solutions, ff .548mesh curve, 448mesh-point, 436mixtures, 202motion, 26Murat’s lemma, 548, 568
N-waves, ff .346, ff .421Newtonian fluid, 47nonconductor of heat, 42nonconservative shocks, ff .264nonresonant curve, 486normal reflection, 589null condition, 115, 143null Lagrangian, 30
oblique reflection, 590
particle, 26periodic solutions, 349, ff .427phase transition, 267, 323piecewise genuinely nonlinear, 284Piola-Kirchhoff stress, 32placement, 26planar elastic oscillations, 198, 214polyconvexity, ff .129porous medium, 142, 143, 190potential flow, 65, 129, 579, ff .580, 585, ff
.588, ff .591potential for wave interaction, 450, 490Poynting vector, 69pressure, XVpressure gradient system, 595pressureless Euler equations, 595pressureless gas, 198production density function, 2propagation of oscillations, 571proper domain, 2pseudopotential, 581pseudoshock, 482pseudovelocity, 581, 582p-system, 198
quasiconvex entropy, 127
radial isentropic gas flow, 203, ff .566, 567,570
random choice method, ff .435
rank-one convex energy, 57Rankine-Hugoniot jump condition, 54, 82rapid oscillations, ff .22rarefaction
front, 481wave, XX, 218, 273, 276, 287wave curve, 218, 239wave spreading, 335, 410, ff .507
reference configuation, 26reference density, 32referential (Lagrangian) formulation, 26referential field equation, 28regular shock reflection, ff .588regularity of solutions
scalar conservation law, ff .188, ff .336systems of n conservation laws, ff .507systems of two conservation laws, ff .415
relaxation, ff .48, ff .108, ff .167motion with, ff .60parameter, 111time, 49via compensated compactness, ff .553
relaxation scheme for scalar conservationlaws, ff .167, ff .553
relaxed system, 111rich systems, 213Riemann invariants, XVII, XIX, XXI, ff
.206, 236coordinate system of, 207, 212, 281, 311
Riemann problem, ff .271multidimensional, ff .573
Riemann solverapproximate, 482simplified, 483
right stretch tensor, 27rotation tensor, 27
sampling point, 439scalar balance law, 12scalar balance law in one space dimension,
ff .358scalar conservation law in multi-space
dimensions, ff .145admissible solutions, ff .148breakdown of classical solutions, ff .146contraction in L1, 149fine structure, ff .180initial-boundary value problem, ff .183via contraction semigroup, ff .158
Subject Index 707
via kinetic formulation, ff .174via layering method, ff .164via relaxation, ff .167via vanishing viscosity, ff .153
scalar conservation law in one spacedimension
admissibility of solutions, 242, 243, 247,249, 257, 292
comparison theorems, ff .350inhomogeneous, ff .365initial data in Lp, 345initial data of compact support, ff .346invariants, 342Lax function, 342, 343N-wave, 347one-sided Lipschitz condition, 336periodic initial data, 349regularity of solutions, ff .336sawtoothed profile, ff .348spreading of rarefaction waves, ff .335via compensated compactness, ff .551via front tracking, ff .478via generalized characteristics, ff .331via relaxation, ff .553
Second Law of thermodynamics, 33self-similar planar irrotational isentropic gas
flow, ff .580self-similar solutions for multidimensional
scalar conservation laws, ff .573separatrix, 329shallow-water equations, XIX, 200shearing, 197shock
admissible, ff .231amplitude of, 232compressive, 241curve, 234delta, 289, 308front, 15, 21generation point of, 335nonconservative, 264of moderate strength, 232overcompressive, 242strength of, 232strong, 232structure of, 254subsonic, 578, 582supersonic, 578, 582transonic, 578, 582
undercompressive, 242weak, 232
shock collision with a steep ramp, 591shock curves coinciding with rarefaction
wave curves, 239, 265, 301, 570shock polar, 578, 582simple waves, XVII, ff .216small disturbance equations, 595solution
admissible, 15, ff .83, ff .87classical, 12, 76measure-valued, ff .549mild, 132nonuniqueness of, ff .82self-similar, ff .271, ff .573, ff .580stability of, ff .116structure for systems, ff .507weak, 12, 21, ff 81
sonic circle, 582sonic speed, 62, 63space-like curve, 378spatial (Eulerian) formulation, 26spatial field equation, 28specific heat, XV, 40specific volume, XV, 197spin tensor, 27standard Riemann semigroup, 477, ff .500state vector, 12strain, 197stress tensor, 32
Cauchy, 32Maxwell, 71Piola-Kirchhoff, 32
stretch tensor, 27stretching tensor, 27strictly hyperbolic, 205subcharacteristic condition, 112, 174, 553symmetrizer, 107symmetry group, 39, 46system
canonical form, 54genuinely nonlinear, ff .214hyperbolic, ff .53of balance laws, ff .12of conservation laws, ff .12rich, 213strictly hyperbolic, ff .203symmetric, 14, 55, 211, 309symmetrizable, 14, 188
708 Subject Index
systems of two conservation lawsinitial data in L1, ff .417initial data with compact support, ff .421local structure of solutions, ff .378N-wave, 422periodic solutions, ff .427regularity of solutions, ff .415sawtoothed profile, 428spreading of rarefaction waves, ff .410via compensated compactness, ff .556via generalized characteristics, ff .373
tame oscillation condition, 502tame variation condition, 514temperature, 33temperature gradient, 34thermal conductivity, 40, 47thermal equations, XXIII, 42thermodynamic admissibility, 34, 43thermodynamic process, 33thermoelastic
fluid, 39, ff .61medium, 36nonconductor of heat, 42, ff .56
thermoelasticity, ff .36thermomechanics, ff .31thermoviscoelastic fluid, 46thermoviscoelasticity, ff .44trace theorem, ff .7traffic theory, ff .195traveling wave, 253, 519, ff .524
umbilic point, 205uniqueness of solutions, ff .501universal gas constant, XV, 40
vacuum state, 289van der Waals gas, 40velocity, 26velocity potential, 65
viscosityartificial, 88bulk, 47–capillarity admissibility criterion, 91of the rate type, 44shear, 47solution, 344vanishing, ff .XXVI, ff .87, ff .153, ff .517,
552viscous
shock admissibility criterion, 254shock profiles, ff .252traveling wave, ff .524wave fan, ff .299
vortex sheets, 63, 64, 577vorticity, 27, 65
waveamplitude, 278approaching, 311, 449, 489breaking, XVII, 78cancellation, amount of, 446centered compression, 335, 415composite, 276compression, 218diffusion, 261elementary, 276interaction, amount of, 311, 445, 451partitioning, 461strength, 278tracing, ff .460transitional, 290virtual, 456, 461viscous, 524
wave fanadmissibility criteria, ff .274interactions, ff .309
Young measure, ff .546, 549, 551, 557, 560,565
Grundlehren dermathematischen Wissenschaften Vol. 325ISBN 978-3-642-04047-4
Constantine M. Dafermos
Hyperbolic Conservation Lawsin Continuum Physics
Publisher’s Erratum
The original eBook version contained a mistake that occurred duringthe production process. This is the corrected eBook.
A Series of Comprehensive Studies in Mathematics
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247. Suzuki: Group Theory I248. Suzuki: Group Theory II249. Chung: Lectures from Markov Processes to Brownian Motion250. Arnold: Geometrical Methods in the Theory of Ordinary Differential Equations251. Chow/Hale: Methods of Bifurcation Theory252. Aubin: Nonlinear Analysis on Manifolds. Monge-Ampère Equations253. Dwork: Lectures on ρ-adic Differential Equations254. Freitag: Siegelsche Modulfunktionen255. Lang: Complex Multiplication256. Hörmander: The Analysis of Linear Partial Differential Operators I257. Hörmander: The Analysis of Linear Partial Differential Operators II258. Smoller: Shock Waves and Reaction-Diffusion Equations259. Duren: Univalent Functions260. Freidlin/Wentzell: Random Perturbations of Dynamical Systems261. Bosch/Güntzer/Remmert: Non Archimedian Analysis – A System Approach to Rigid
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Advanced Theory and Bundle Methods307. Schwarz: Quantum Field Theory and Topology308. Schwarz: Topology for Physicists309. Adem/Milgram: Cohomology of Finite Groups310. Giaquinta/Hildebrandt: Calculus of Variations I: The Lagrangian Formalism311. Giaquinta/Hildebrandt: Calculus of Variations II: The Hamiltonian Formalism312. Chung/Zhao: From Brownian Motion to Schrödinger’s Equation313. Malliavin: Stochastic Analysis314. Adams/Hedberg: Function spaces and Potential Theory315. Bürgisser/Clausen/Shokrollahi: Algebraic Complexity Theory316. Saff/Totik: Logarithmic Potentials with External Fields317. Rockafellar/Wets: Variational Analysis318. Kobayashi: Hyperbolic Complex Spaces319. Bridson/Haefliger: Metric Spaces of Non-Positive Curvature320. Kipnis/Landim: Scaling Limits of Interacting Particle Systems321. Grimmett: Percolation322. Neukirch: Algebraic Number Theory323. Neukirch/Schmidt/Wingberg: Cohomology of Number Fields
325. Dafermos: Hyperbolic Conservation Laws in Continuum Physics326. Waldschmidt: Diophantine Approximation on Linear Algebraic Groups327. Martinet: Perfect Lattices in Euclidean Spaces328. Van der Put/Singer: Galois Theory of Linear Differential Equations329. Korevaar: Tauberian Theory. A Century of Developments330. Mordukhovich: Variational Analysis and Generalized Differentiation I: Basic Theory331. Mordukhovich: Variational Analysis and Generalized Differentiation II: Applications
324. Liggett: Stochastic Interacting Systems: Contact, Voter and Exclusion Processes
Derived Categories332. Kashiwara/Schapira: Categories and Sheaves. An Introduction to Ind-Objects and
334. Sernesi: Deformations of Algebraic Schemes335. Bushnell/Henniart: The Local Langlands Conjecture for GL(2)
333. Grimmett: The Random-Cluster Model
336. Gruber: Convex and Discrete Geometry337.
338. Villani: Optimal Transport: Old and New
Maz'ya/Shaposhnikova: Theory of Sobolev Multipliers. With Applications to Differentialand Integral Operators
