A note on entropy solutions for degenerate parabolic equations with L-1 boolean AND L-p data

被引：2

作者：

Bendahmane, Mostafa ^{[1
]}

Karlsen, Kenneth Hvistendahl ^{[2
]}

机构：

[1] Univ Victor Segalen Bordeaux 2, Inst Math Bordeaux, F-33076 Bordeaux, France

[2] Univ Oslo, Dept Math, Ctr Math Applicat, POB 1053, N-0316 Oslo, Norway

来源：

INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS | 2012年 / 4卷 / 1-2期

关键词：

degenerate parabolic equation; quasilinear; anisotropic diffusion; entropy solution; uniqueness; existence;

D O I：

10.1504/IJDSDE.2012.045996

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove existence and uniqueness results for entropy solutions of degenerate parabolic equations with appropriately growing nonlinearities and unbounded initial data.

引用

页码：78 / 92

页数：15

共 29 条

[1] DISCRETE DUALITY FINITE VOLUME SCHEMES FOR DOUBLY NONLINEAR DEGENERATE HYPERBOLIC-PARABOLIC EQUATIONS
Andreianov, B.
Bendahmane, M.
Karlsen, K. H.
[J]. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2010, 7 (01) : 1 - 67
[2] Andreianov B., 2009, J DIFFER EQUATIONS, V247
[3] Renormalized entropy solutions for quasi-linear anisotropic degenerate parabolic equations
Bendahmane, M
Karlsen, KH
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2004, 36 (02) : 405 - 422
[4] BENILAN P, 1995, ANN I H POINCARE-AN, V12, P727
[5] On strongly degenerate convection-diffusion problems modeling sedimentation-consolidation processes
Bürger, R
Evje, S
Karlsen, KH
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 247 (02) : 517 - 556
[6] ON THE UNIQUENESS OF THE SOLUTION OF THE EVOLUTION DAM PROBLEM
CARRILLO, J
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 22 (05) : 573 - 607
[7] Entropy solutions for nonlinear degenerate problems
Carrillo, J
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1999, 147 (04) : 269 - 361
[8] L1-framework for continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations
Chen, GQ
Karlsen, KH
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 358 (03) : 937 - 963
[9] Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations
Chen, GQ
Perthame, B
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2003, 20 (04): : 645 - 668
[10] Stability of entropy solutions to the Cauchy problem for a class of nonlinear hyperbolic-parabolic equations
Chen, GQ
Dibenedetto, E
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2001, 33 (04) : 751 - 762

← 1 2 3 →