Decay estimates to equilibrium for some asymptotically autonomous semilinear evolution equations

被引：24

作者：

Ben Hassen, Imen ^{[1
]}

机构：

[1] Fac Sci Bizerte, Dept Math, Jarzouna 7021, Bizerte, Tunisia

来源：

ASYMPTOTIC ANALYSIS | 2010年 / 69卷 / 1-2期

关键词：

convergence; rate of decay; analytic nonlinearity; nonautonomous; evolution equation; GRADIENT-LIKE SYSTEMS; ANALYTIC NONLINEARITY; BOUNDED SOLUTIONS; WAVE-EQUATION; CONVERGENCE; DISSIPATION;

D O I：

10.3233/ASY-2010-0994

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We estimate the rate of decay of the difference between a solution and its limiting equilibrium for the nonautonomous first-order problem (u) over dot + Mu = g(t), t is an element of R(+), and for the second-order problem (u) over dot + (u) over dot + Mu = g(t), t is an element of R(+), where M is a gradient operator and g is a function which tends to 0 when t tends to infinity.

引用

页码：31 / 44

页数：14

共 16 条

[1]

[Anonymous], 1992, ACTA MATH U COMENIAN

[2]

Brunovsky P, 1997, Z ANGEW MATH PHYS, V48, P976

[3] Convergence to steady states in asymptotically autonomous semilinear evolution equations [J].

Chill, R ;

Jendoubi, MA .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 53 (7-8) :1017-1039

[4] CONVERGENCE IN GRADIENT-LIKE SYSTEMS WITH APPLICATIONS TO PDE [J].

HALE, JK ;

RAUGEL, G .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1992, 43 (01) :63-124

[5] On the convergence of global and bounded solutions of some evolution equations [J].

Haraux, A. ;

Jendoubi, M. A. .

JOURNAL OF EVOLUTION EQUATIONS, 2007, 7 (03) :449-470

[6] Convergence of bounded weak solutions of the wave equation with dissipation and analytic nonlinearity [J].

Haraux, A ;

Jendoubi, MA .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1999, 9 (02) :95-124

[7]

Haraux A, 2001, ASYMPTOTIC ANAL, V26, P21

[8] Convergence in gradient-like systems which are asymptotically autonomous and analytic [J].

Huang, SZ ;

Takác, P .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 46 (05) :675-698

[9] Convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity [J].

Jendoubi, MA .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 144 (02) :302-312

[10] A simple unified approach to some convergence theorems of L. Simon [J].

Jendoubi, MA .

JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 153 (01) :187-202

← 1 2 →