Quasi-linear diffusion equations with gradient tenns and L1 data

被引：3

作者：

Andreu, F ^{[1
]}

de León, SS ^{[1
]}

Toledo, J ^{[1
]}

机构：

[1] Univ Valencia, Dept Math Anal, E-46100 Valencia, Spain

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2004年 / 56卷 / 08期

关键词：

nonlinear diffusion equations; global existence; generalized solutions;

D O I：

10.1016/j.na.2003.11.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we study the following quasi-linear parabolic problem: mu(t) - Deltau + \u\(beta-2) u\delu\(q) = \u\(alpha-2) \delu\(p) in Omega x ]0, T[, u(x, t) = 0 on phiOmega x]0, T[, u(x,0) = u(0)(x) in Omega, where Omega is a bounded open set of R-N and T > 0. We prove that if alpha, beta > 1, 0 less than or equal to p < q, 1 less than or equal to q less than or equal to 2, and alpha + p < beta + q, then there exists a generalized solution for all u(0) is an element of L-1 (Omega). (C) 2003 Elsevier Ltd. All rights reserved.

引用

页码：1175 / 1209

页数：35

共 20 条

[1] Global existence for a degenerate nonlinear diffusion problem with nonlinear gradient term and source [J].

Andreu, F ;

Mazón, JM ;

Simondon, F ;

Toledo, J .

MATHEMATISCHE ANNALEN, 1999, 314 (04) :703-728

[2] Existence results for L1 data of some quasi-linear parabolic problems with a quadratic gradient term and source [J].

Andreu, F ;

De Léon, SS ;

Boccardo, L ;

Orsina, L .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (01) :1-16

[3] Existence and uniqueness for a degenerate parabolic equation with L1-data [J].

Andreu, F ;

Mazón, JM ;

De León, SS ;

Toledo, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 351 (01) :285-306

[4] Degenerate parabolic equations with initial data measures [J].

Andreucci, D .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (10) :3911-3923

[5]

Benilan P., 1995, ANN SCUOLA NORM-SCI, V22, P241

[6] NON-LINEAR ELLIPTIC AND PARABOLIC EQUATIONS INVOLVING MEASURE DATA [J].

BOCCARDO, L ;

GALLOUET, T .

JOURNAL OF FUNCTIONAL ANALYSIS, 1989, 87 (01) :149-169

[7] EXISTENCE RESULTS FOR SOME QUASILINEAR PARABOLIC EQUATIONS [J].

BOCCARDO, L .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1989, 13 (04) :373-392

[8] SOME BLOWUP RESULTS FOR A NONLINEAR PARABOLIC EQUATION WITH A GRADIENT TERM [J].

CHIPOT, M ;

WEISSLER, FB .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (04) :886-907

[9] REMARKS ON BLOW UP FOR A NONLINEAR PARABOLIC EQUATION WITH A GRADIENT TERM [J].

FILA, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 111 (03) :795-801

[10] ON THE EXISTENCE OF WEAK SOLUTIONS FOR QUASILINEAR PARABOLIC INITIAL-BOUNDARY VALUE-PROBLEMS [J].

LANDES, R .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1981, 89 :217-237

← 1 2 →