Attractors for the nonclassical diffusion equations with fading memory

被引：31

作者：

Wang, Xuan ^{[1
]}

Yang, Lu ^{[2
]}

Zhong, Chengkui ^{[2
,3
]}

机构：

[1] NW Normal Univ, Coll Math & Informat Sci, Lanzhou 730070, Peoples R China

[2] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

[3] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 362卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Nonclassical diffusion equation; Global attractor; Critical exponent; Fading memory; DAMPED WAVE-EQUATION; GLOBAL ATTRACTORS; ASYMPTOTIC REGULARITY; HYPERBOLIC EQUATION; DYNAMICS;

D O I：

10.1016/j.jmaa.2009.09.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss long-time dynamical behavior of the nonclassical diffusion equation with fading memory when nonlinearity is critical. The existence and regularity of global attractors in weak topological space and strong topological space are obtained, while the forcing term only belongs to H-1(Omega) and L-2(Omega) respectively. The results in this part are new and appear to be optimal corresponding to the forcing term. (C) 2009 Published by Elsevier Inc.

引用

页码：327 / 337

页数：11

共 20 条

[1] ON THE PROBLEM OF DIFFUSION IN SOLIDS [J].

AIFANTIS, EC .

ACTA MECHANICA, 1980, 37 (3-4) :265-296

[2]

[Anonymous], 2001, Adv. Math. Sci. Appl.

[3]

[Anonymous], ACTA MATH APPL SIN

[4] A DAMPED HYPERBOLIC EQUATION WITH CRITICAL EXPONENT [J].

ARRIETA, J ;

CARVALHO, AN ;

HALE, JK .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1992, 17 (5-6) :841-866

[5]

Borini S, 1999, ASYMPTOTIC ANAL, V20, P263

[6] ON A THEORY OF HEAT CONDUCTION INVOLVING 2 TEMPERATURES [J].

CHEN, PJ .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1968, 19 (04) :614-&

[7]

CHOLEWA JW, 2001, GLOBAL ATTRACTORS AB

[8]

DAFERMOS CM, 1970, ARCH RATION MECH AN, V37, P297

[9] Attractors for semi-linear equations of viscoelasticity with very low dissipation [J].

Gatti, S. ;

Miranville, A. ;

Pata, V. ;

Zelik, S. .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2008, 38 (04) :1117-1138

[10] Global attractors for a semilinear hyperbolic equation in viscoelasticity [J].

Giorgi, C ;

Rivera, JEM ;

Pata, V .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 260 (01) :83-99

← 1 2 →