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

共 50 条

[1] Asymptotic Compactness and Attractors for Phase-Field Equations in ℝ3
Francisco Morillas
José Valero
Set-Valued Analysis, 2008, 16 : 861 - 897
[2] ATTRACTORS FOR A CAGINALP PHASE-FIELD MODEL TYPE ON THE WHOLE SPACE R3
Bangola, Brice Doumbe
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2012, 2 (03): : 251 - 272
[3] Robust unbounded attractors for differential equations in R3
Homburg, Ale Jan
Mramor, Blaz
PHYSICA D-NONLINEAR PHENOMENA, 2010, 239 (3-4) : 202 - 206
[4] Discrete compactness and the approximation of Maxwell's equations in R3
Monk, P
Demkowicz, L
MATHEMATICS OF COMPUTATION, 2001, 70 (234) : 507 - 523
[5] Attractors of multivalued dynamical processes generated by phase-field equations
Kapustyan, AV
Melnik, VS
Valero, J
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (07): : 1969 - 1983
[6] Attractors for semilinear strongly damped wave equations on R3
Belleri, V
Pata, V
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2001, 7 (04) : 719 - 735
[7] ROBUST EXPONENTIAL ATTRACTORS FOR SINGULARLY PERTURBED PHASE-FIELD TYPE EQUATIONS
Miranville, Alain
Zelik, Sergey
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2002,
[8] Maximal attractors for the phase-field equations of Penrose-Fife type
Shen, WX
Zheng, SM
APPLIED MATHEMATICS LETTERS, 2002, 15 (08) : 1019 - 1023
[9] Asymptotic profiles for the second grade fluids equations in R3
Coulaud, Olivier
DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, 2014, 11 (02) : 125 - 165
[10] Asymptotic smoothing and attractors for the generalized Benjamin-Bona-Mahony equation on R3
Stanislavova, M
Stefanov, A
Wang, BX
JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 219 (02) : 451 - 483

← 1 2 3 4 5 →