GLOBAL WELL-POSEDNESS IN UNIFORMLY LOCAL SPACES FOR THE CAHN-HILLIARD EQUATION IN R3

被引：10

作者：

Zelik, Sergey ^{[1
]}

Pennant, Jon ^{[1
]}

机构：

[1] Univ Surrey, Guildford GU2 7XH, Surrey, England

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2013年 / 12卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Cahn-Hilliard equation; unbounded domains; infinite-energy solutions; SPATIALLY NONDECAYING SOLUTIONS; REACTION-DIFFUSION SYSTEMS; EXPONENTIAL ATTRACTORS; ASYMPTOTIC-BEHAVIOR; EVOLUTION-EQUATIONS;

D O I：

10.3934/cpaa.2013.12.461

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the infinite-energy solutions of the Cahn-Hilliard equation in the whole 3D space in uniformly local phase spaces. In particular, we establish the global existence of solutions for the case of regular potentials of arbitrary polynomial growth and for the case of sufficiently strong singular potentials. For these cases, the uniqueness and further regularity of the obtained solutions are proved as well. We discuss also the analogous problems for the case of the so-called Cahn-Hilliard-Oono equation where, in addition, the dissipativity of the associated solution semigroup is established

引用

页码：461 / 480

页数：20

共 39 条

[1] EXISTENCE AND FINITE DIMENSIONALITY OF THE GLOBAL ATTRACTOR FOR EVOLUTION-EQUATIONS ON UNBOUNDED-DOMAINS
ABERGEL, F
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1990, 83 (01) : 85 - 108
[2] [Anonymous], 1992, STUD MATH APPL
[3] [Anonymous], 1989, Internat. Ser. Numer. Math, DOI DOI 10.1007/978-3-0348-9148-6_3
[4] ATTRACTORS OF PARTIAL-DIFFERENTIAL EVOLUTION-EQUATIONS IN AN UNBOUNDED DOMAIN
BABIN, AV
VISHIK, MI
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1990, 116 : 221 - 243
[5] BABIN AV, 2006, HDB DYNAMICAL SYST B, V1, P983
[6] Finite-dimensional attractor for the viscous Cahn-Hilliard equation in an unbounded domain
Bonfoh, A
[J]. QUARTERLY OF APPLIED MATHEMATICS, 2006, 64 (01) : 93 - 104
[7] Bricmont J, 1999, COMMUN PUR APPL MATH, V52, P839, DOI 10.1002/(SICI)1097-0312(199907)52:7<839::AID-CPA4>3.0.CO
[8] 2-I
[9] Caffarelli L., 1995, RCH RATIONAL MECH AN, V133, P129
[10] FREE ENERGY OF A NONUNIFORM SYSTEM .1. INTERFACIAL FREE ENERGY
CAHN, JW
HILLIARD, JE
[J]. JOURNAL OF CHEMICAL PHYSICS, 1958, 28 (02) : 258 - 267

← 1 2 3 4 →