[1] Antonic N, Lazar M. H-measures and variants applied to parabolic equations. J Math Anal Appl, 2008, 343(1): 207--225
[2] Dacorogna B. Weak Continuity and Weak Lower Semicontinuity of Nonlinear Functionals. Lecture Notes in Mathematics, Vol 922. Berlin: Springer, 1982
[3] DiPerna R J. Measure-valued solutions to conservation laws. Arch Ration Mech Anal, 1985, 88(3): 223--270
[4] Gerard P. Microlocal defect measures. Comm Partial Differential Equations, 1991, 16(11): 1761--1794
[5] Hille E, Phillips R S. Functional Analysis and Semi-Groups. American Mathematical Society Colloquium Publications, Vol 31.
Providence RI: American Mathematical Society, 1957
[6] Karlsen K H, Risebro N H, Towers J D. L1 stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients. Skr K Nor Vidensk Selsk, 2003, (3): 1--49
[7] Karlsen K H, Risebro N H, Towers J D. Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient. IMA J Numer Anal, 2002, 22(4): 623--664
[8] Karlsen K H, Towers J D. Convergence of the Lax--Friedrichs scheme and stability for conservation laws with a discontinous space-time dependent flux. Chinese Ann Math Ser B, 2004, 25(3): 287--318
[9] Karlsen K H, Rascle M, Tadmor E. On the existence and compactness of a two-dimensional resonant system of conservation laws.
Commun Math Sci, 2007, 5(2): 253--265
[10] Kruzkov S N. First order quasilinear equations with several independent variables. Mat Sb (N S), 1970, 81(123): 228--255
[11] Ladyzhenskaya O A, Ural'ceva N N. Linear and Quasilinear Elliptic Equations. New York: Academic Press, 1968
[12] Lions P -L, Perthame B, Tadmor E. A kinetic formulation of multidimensional scalar conservation laws and related equations. J Amer Math Soc, 1994, 7(1): 169--191
[13] Panov E Yu. On sequences of measure-valued solutions of a first-order quasilinear equation. Mat Sb, 1994, 185(2): 87--106
[14] Panov E Yu. On the strong precompactness of bounded sets of measure-valued solutions of a first-order quasilinear equation.
Mat Sb, 1995, 186(5): 103--114
[15] Panov E Yu. Property of strong precompactness for bounded sets of measure-valued solutions of a first-order quasilinear equation.
Mat Sb, 1999, 190(3): 427--446
[16] Panov E Yu. Ultra-parabolic equations with rough coefficients. Entropy solutions and strong precompactness property. Journal of Mathematical Sciences, 2009, 159(2): 180--228
[17] Panov E Yu. Existence and strong precompactness properties for entropy solutions of a first-order quasilinear equation with discontinuous flux. Arch Ration Mech Anal, 2009, doi:10.1007/s00205-009-0217-x
[18] Panov E Yu. On the strong pre-compactness property for entropy solutions of a degenerate elliptic equation with discontinuous flux.
J Differ Equ, 2009, 247: 2821--2870
[19] Sazhenkov S A. The genuinely nonlinear Graetz--{N}usselt ultraparabolic equation. Sibirsk Mat Zh, 2006, 47(2): 431--454
[20] Stein E M. Singular Integrals and Differentiability Properties of Functions. Princeton Mathematical Series, No 30. Princeton NJ: Princeton University Press, 1970
[21] Tadmor E, Tao T. Velocity averaging, kinetic formulations, and regularizing effects in quasi-linear partial differential equations.
Commun Pure Appl Math, 2008, 61: 1--34
[22] Tartar L. Compensated compactness and applications to partial differential equations Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol IV. Boston, Mass: Pitman, 1979: 136--212
[23] Tartar L. H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations. Proc Roy Soc Edinburgh Sect A, 1990, 115(3/4): 193--230
|