Geodesic
Property of strong precompactness for bounded sets of measure-valued solutions of a first-order quasilinear equation
Sbornik. Mathematics, Tome 190 (1999) no. 3, pp. 427-446 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Sequences of measure-valued solutions of a non-degenerate quasilinear equation of the first order are shown to be strongly precompact in the general case, when the flow functions contain independent variables and are merely continuous. 
@article{SM_1999_190_3_a3,
     author = {E. Yu. Panov},
     title = {Property of strong precompactness for bounded sets of measure-valued solutions of a~first-order quasilinear equation},
     journal = {Sbornik. Mathematics},
     pages = {427--446},
     year = {1999},
     volume = {190},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_3_a3/}
}
TY  - JOUR
AU  - E. Yu. Panov
TI  - Property of strong precompactness for bounded sets of measure-valued solutions of a first-order quasilinear equation
JO  - Sbornik. Mathematics
PY  - 1999
SP  - 427
EP  - 446
VL  - 190
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1999_190_3_a3/
LA  - en
ID  - SM_1999_190_3_a3
ER  - 
%0 Journal Article
%A E. Yu. Panov
%T Property of strong precompactness for bounded sets of measure-valued solutions of a first-order quasilinear equation
%J Sbornik. Mathematics
%D 1999
%P 427-446
%V 190
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1999_190_3_a3/
%G en
%F SM_1999_190_3_a3
E. Yu. Panov. Property of strong precompactness for bounded sets of measure-valued solutions of a first-order quasilinear equation. Sbornik. Mathematics, Tome 190 (1999) no. 3, pp. 427-446. http://geodesic.mathdoc.fr/item/SM_1999_190_3_a3/

[1] Tartar L., “Compensated compactness and applications to partial differential equations”, Nonlinear analysis and mechanics, Heriot-Watt Symp., Vol. 4 (Edinburgh, 1979), Res. Notes Math., 39, 1979, 136–212 | MR | Zbl

[2] Panov E. Yu., “O posledovatelnostyakh meroznachnykh reshenii kvazilineinogo uravneniya pervogo poryadka”, Matem. sb., 185:2 (1994), 87–106 | MR | Zbl

[3] Panov E. Yu., “O silnoi predkompaktnosti ogranichennykh mnozhestv meroznachnykh reshenii kvazilineinogo uravneniya pervogo poryadka”, Matem. sb., 186:5 (1995), 103–114 | MR | Zbl

[4] Lions P. L., Perthame B., Tadmor E., “A kinetic formulation of multidimensional scalar conservation laws and related equations”, J. Amer. Math. Soc., 7:1 (1994), 169–191 | DOI | MR | Zbl

[5] Kruzhkov S. N., “Obobschennye resheniya zadachi Koshi v tselom dlya nelineinykh uravnenii pervogo poryadka”, Dokl. AN SSSR, 187:1 (1969), 29–32 | Zbl

[6] Kruzhkov S. N., “Kvazilineinye uravneniya pervogo poryadka so mnogimi nezavisimymi peremennymi”, Matem. sb., 81:2 (1970), 228–255 | MR | Zbl

[7] DiPerna R. J., “Measure-valued solutions to conservation laws”, Arch. Rational Mech. Anal., 88 (1985), 223–270 | DOI | MR | Zbl

[8] Dakoronya B., “Slabaya nepreryvnost i slabaya polunepreryvnost snizu nelineinykh funktsionalov”, UMN, 44:4 (1989), 35–98 | MR

[9] Tartar L., “$H$-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations”, Proc. Roy. Soc. Edinburgh. Sect. A, 115:3–4 (1990), 193–230 | MR | Zbl

[10] Berg I., Lefstrem I., Interpolyatsionnye prostranstva, Mir, M., 1980 | MR