On a phase transition model

被引：12

作者：

Byeon, Jaeyoung ^{[1
]}

Rabinowitz, Paul H. ^{[1
,2
]}

机构：

[1] POSTECH, Dept Math, Pohang 790784, Kyungbuk, South Korea

[2] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2013年 / 47卷 / 1-2期

基金：

新加坡国家研究基金会;

关键词：

ALLEN-CAHN EQUATIONS; STATIONARY LAYERED SOLUTIONS; PERIODIC MEDIA; ELLIPTIC PROBLEMS; MIXED STATES; R-N; R-2; MULTIPLICITY; MINIMIZERS; BANGERT;

D O I：

10.1007/s00526-012-0507-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An Allen-Cahn phase transition model with a periodic nonautonomous term is presented for which an infinite number of transition states is shown to exist. A constrained minimization argument and the analysis of a limit problem are employed to get states having a finite number of transitions. A priori bounds and an approximation procedure give the general case. Decay properties are also studied and a sharp transition result with an arbitrary interface is proved.

引用

页码：1 / 23

页数：23

共 25 条

[1]

Alessio F, 2000, CALC VAR PARTIAL DIF, V11, P177, DOI 10.1007/s005260000036

[2] Entire solutions in R2 for a class of Allen-Cahn equations [J].

Alessio, F ;

Montecchiari, P .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2005, 11 (04) :633-672

[3]

Alessio F, 2005, ADV NONLINEAR STUD, V5, P515

[4] Existence of infinitely many stationary layered solutions in R2 for a class of periodic Allen-Cahn equations [J].

Alessio, F ;

Jeanjean, L ;

Montecchiari, P .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2002, 27 (7-8) :1537-1574

[5]

[Anonymous], 1990, Variational Methods: Applications to Non-linear Partial Differential Equations and Hamiltonian Systems

[6]

BANGERT V, 1989, ANN I H POINCARE-AN, V6, P95

[7] Many solutions of elliptic problems on Rn of irrational slope [J].

Bessi, U .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2005, 30 (12) :1773-1804

[8] Slope-changing solutions of elliptic problems on Rn [J].

Bessi, Ugo .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (12) :3923-3947

[9] Planelike minimizers in periodic media [J].

Caffarelli, LA ;

De La Llave, R .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2001, 54 (12) :1403-1441

[10] Multiplicity results for interfaces of Ginzburg-Landau-Allen-Cahn equations in periodic media [J].

de la Llave, Rafael ;

Valdinoci, Enrico .

ADVANCES IN MATHEMATICS, 2007, 215 (01) :379-426

← 1 2 3 →