On the Lojasiewicz-Simon gradient inequality

被引：115

作者：

Chill, R ^{[1
]}

机构：

[1] Univ Ulm, Abt Angew Anal, D-89069 Ulm, Germany

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2003年 / 201卷 / 02期

关键词：

Lojasiewicz-Simon inequality; asymptotic behaviour; convergence to equilibrium; gradient-like evolution equation; semilinear diffusion equation; semilinear wave equation; Cahn-Hilliard equation; Kirchhoff-Carrier equation; quasilinear equation;

D O I：

10.1016/S0022-1236(02)00102-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a general version of the Lojasiewicz-Simon inequality, and we show how to apply the abstract result to study energy functionals E of the form E(nu) = 1/2a(nu, nu) + integral(Omega) F(x, nu), defined on a Hilbert space V --> L-2 (Omega). We show that in some cases it is possible to prove the Lojasiewicz-Simon inequality for such functionals without the assumption of analyticity. The results apply to study the asymptotic behaviour of parabolic and hyperbolic evolution equations. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：572 / 601

页数：30

共 35 条

[1]

AULBACH B, 1984, LECT NOTES MATH, V1058, pU1

[2] Long-time vanishing properties of solutions of some semilinear parabolic equations [J].