Asymptotic Compactness and Attractors for Phase-Field Equations in ℝ3

被引：0

作者：

Francisco Morillas

José Valero

机构：

[1] Universidad Politécnica de Valencia,Dpto. de Ingeniería Hidráulica y Medio Ambiente

[2] Universidad Miguel Hernández,Centro de Investigación Operativa

来源：

Set-Valued Analysis | 2008年 / 16卷

关键词：

Setvalued dynamical system; Global attractor; Phase-field equations; Unbounded domain; 35B40; 35B41; 35K55; 35K57; 37B25; 58C06;

D O I：

暂无

中图分类号：

学科分类号：

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 non-linear 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：36

共 50 条

[21] Uniform attractors for a phase-field model with memory and quadratic nonlinearity
Giorgi, C
Grasselli, M
Pata, V
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1999, 48 (04) : 1395 - 1445
[22] On the asymptotic behavior of a phase-field model for elastic phase transitions
Kalies W.D.
Journal of Dynamics and Differential Equations, 1997, 9 (2) : 289 - 306
[23] Asymptotic solutions of a phase-field model or alloy solidification
Clemons, CB
Hariharan, SI
Young, GW
SIAM JOURNAL ON APPLIED MATHEMATICS, 2002, 62 (06) : 1952 - 1979
[24] Asymptotic justification of the conserved phase-field model with memory
Felli, V
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2000, 19 (04): : 953 - 976
[25] Asymptotic behavior of a generalization of the Caginalp phase-field system
Conti, Monica
Dell'Oro, Filippo
Miranville, Alain
ASYMPTOTIC ANALYSIS, 2013, 81 (3-4) : 297 - 314
[26] Compactness and long-time stabilization of solutions to phase-field models
Aizicovici, S
Petzeltová, H
ANALYSIS AND OPTIMIZATION OF DIFFERENTIAL SYSTEMS, 2003, 121 : 1 - 12
[27] A note on the summation relation in phase-field equations
Haghani, Reza
Erfani, Hamidreza
McClure, James E.
Berg, Carl Fredrik
PHYSICS OF FLUIDS, 2023, 35 (09)
[28] The singular limit dynamics of the phase-field equations
Ahmed Bonfoh
Annali di Matematica Pura ed Applicata, 2011, 190 : 105 - 144
[29] The singular limit dynamics of the phase-field equations
Bonfoh, Ahmed
ANNALI DI MATEMATICA PURA ED APPLICATA, 2011, 190 (01) : 105 - 144
[30] Robust exponential attractors for a parabolic-hyperbolic phase-field system
Enyi, Cyril D.
BOUNDARY VALUE PROBLEMS, 2018,

← 1 2 3 4 5 →