A DOUBLY NONLINEAR PARABOLIC EQUATION WITH A SINGULAR POTENTIAL

被引：3

作者：

Cherfils, Laurence ^{[1
]}

Gatti, Stefania ^{[2
]}

Miranville, Alain ^{[3
]}

机构：

[1] Univ La Rochelle, Lab MIA, Ave Michel Crepeau, F-17042 La Rochelle, France

[2] Univ Modena & Reggio Emilia, Dipartimento Matemat, I-41100 Modena, Italy

[3] Univ Poitiers, Lab Math & Applicat, UMR CNRS 6086, SP2MI, F-86962 Futuroscope, France

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2011年 / 4卷 / 01期

关键词：

Doubly nonlinear equation; singular potential; global attractor; exponential attractor;

D O I：

10.3934/dcdss.2011.4.51

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our aim in this paper is to study the long time behavior, in terms of finite dimensional attractors, of doubly nonlinear Allen-Cahn type equations with singular potentials.

引用

页码：51 / 66

页数：16

共 13 条

[1]

[Anonymous], 1992, Studies in Mathematics and its Applications

[2]

[Anonymous], 1967, Linear and Quasilinear Equations of Parabolic Type

[3]

[Anonymous], 1994, Exponential attractors for dissipative evolution equations

[4] Existence of global solutions to the Caginalp phase-field system with dynamic boundary conditions and singular potentials (vol 343, pg 557, 2008) [J].

Cherfils, Laurence ;

Gatti, Stefania ;

Miranville, Alain .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 348 (02) :1029-1030

[5] Existence of global solutions to the Caginalp phase-field system with dynamic boundary conditions and singular potentials [J].

Cherfils, Laurence ;

Gatti, Stefania ;

Miranville, Alain .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 343 (01) :557-566

[6] EXPONENTIAL ATTRACTORS FOR A DOUBLY NONLINEAR EQUATION [J].

EDEN, A ;

RAKOTOSON, JM .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1994, 185 (02) :321-339

[7]

Eden A., 1991, J DYN DIFFER EQU, V3, P87

[8] Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance [J].

Gurtin, ME .

PHYSICA D-NONLINEAR PHENOMENA, 1996, 92 (3-4) :178-192

[9] Large time behavior via the method of l-trajectories [J].

Málek, J ;

Prazák, D .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 181 (02) :243-279

[10] Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type [J].

Miranville, A. ;

Zelik, S. .

NONLINEARITY, 2007, 20 (08) :1773-1797

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