Asymptotic Compactness and Attractors for Phase-Field Equations in R3

被引：3

作者：

Morillas, Francisco ^{[1
]}

Valero, Jose ^{[2
]}

机构：

[1] Univ Politecn Valencia, Dpto Ingn Hidraul & Medio Ambiente, Valencia 46022, Spain

[2] Univ Miguel Hernandez, Ctr Invest Operat, Alicante 03202, Spain

来源：

SET-VALUED ANALYSIS | 2008年 / 16卷 / 7-8期

关键词：

Setvalued dynamical system; Global attractor; Phase-field equations; Unbounded domain;

D O I：

10.1007/s11228-008-0096-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the asymptotic behaviour of solutions of the phase-field system on an unbounded domain. We do not assume conditions on the nonlinear term ensuring the uniqueness of the Cauchy problem, so that we have to work with multivalued semiflows rather than with semigroups of operators. In this way we prove the existence of a global attractor by considering the convergence in an appropriate weighted space. This result is also new for more restrictive conditions, which guarantee the uniqueness of solutions.

引用

页码：861 / 897

页数：37

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