Entropy Solution for a Nonlinear Degenerate Parabolic Problem in Weighted Sobolev Space via Rothe's Time-discretization Approach

被引：0

作者：

Sabri, Abdelali ^{[1
]}

Jamea, Ahmed ^{[2
]}

机构：

[1] Hassan First Univ, Dept Econ, Fac Econ & Management, BP 764, Settat, Morocco

[2] CRMEF Casablanca Settat, Equipe STIE, El Jadida, Morocco

来源：

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA | 2023年 / 41卷

关键词：

Degenerate parabolic problem; entropy solution; existence; semi-discretization; Rothe's method; uniqueness; weighted Sobolev space; ELLIPTIC-EQUATIONS;

D O I：

10.5269/bspm.63558

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove the existence and uniqueness results of an entropy solution to a class of nonlinear degenerate parabolic problem with Dirichlet-type boundary condition and L1 data. The main tool used here is the Rothe's time-discretization approach combined with the theory of weighted Sobolev spaces.

引用

页数：14

共 16 条

[1]

Abassi A., 2008, INT J MATH STAT, V2, P4

[2]

Benilan P., 1995, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), V22, P241

[3]

BOCCARDO L, 1992, COMMUN PART DIFF EQ, V17, P641

[4] STRONGLY NONLINEAR ELLIPTIC-EQUATIONS HAVING NATURAL GROWTH TERMS AND L(1) DATA [J].

BOCCARDO, L ;

GALLOUET, T .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1992, 19 (06) :573-579

[5] Existence and uniqueness of solutions for some degenerate nonlinear Dirichlet problems [J].

Cavalheiro, Albo Carlos .

JOURNAL OF APPLIED ANALYSIS, 2013, 19 (01) :41-54

[6] Weighted Sobolev Spaces and Degenerate Elliptic Equations [J].

Cavalheiro, Albo Carlos .

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2008, 26 (1-2) :117-132

[7] Variable exponent, linear growth functionals in image restoration [J].

Chen, Yunmei ;

Levine, Stacey ;

Rao, Murali .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2006, 66 (04) :1383-1406

[8] Pseudo-monotonicity and degenerated or singular elliptic operators [J].

Drabek, P ;

Kufner, A ;

Mustonen, V .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1998, 58 (02) :213-221

[9]

El Hachimi A, 2007, ELECTRON J QUAL THEO, P1

[10]

GAGNEUX G, 1996, MATH APPL, V22

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