Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity

被引：18

作者：

Bonheure, D ^{[1
]}

机构：

[1] Catholic Univ Louvain, Inst Matemat Pure & Appl, B-1348 Louvain, Belgium

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2004年 / 21卷 / 03期

关键词：

multitransition heteroclinics and homoclinics; Swift-Hohenberg equation; minimization; saddle-focus equilibrium;

D O I：

10.1016/S0294-1449(03)00037-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence of stationary solutions of a class of diffusion equations related to the so-called extended Fisher-Kolmogorov equation and the Swift-Hohenberg equation. We prove the existence of multitransition kinks and pulses. These solutions are obtained as local minima of the associated functional. For the Swift-Hohenberg equation, our result partially proves a numerical conjecture. (C) 2003 Elsevier SAS. All rights reserved.

引用

页码：319 / 340

页数：22

共 20 条

[1]

Adams R., 1975, Sobolev space

[2] Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equation [J].

Bonheure, D ;

Sanchez, L ;

Tarallo, M ;

Terracini, S .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2003, 17 (04) :341-356

[3]

BONHEURE D, IN PRESS ATT SEM MAT

[4]

Brezis H., 1999, Analyse fonctionnelle: Theorie et applications

[5] BISTABLE SYSTEMS WITH PROPAGATING FRONTS LEADING TO PATTERN-FORMATION [J].

DEE, GT ;

VANSAARLOOS, W .

PHYSICAL REVIEW LETTERS, 1988, 60 (25) :2641-2644

[6]

Gomper G., 1994, PHASE TRANSITIONS CR

[7]

HABETS P, 2001, CD ROM P EQ 10 PRAG

[8] Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria [J].

Kalies, WD ;

Kwapisz, J ;

VanderVorst, RCAM .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1998, 193 (02) :337-371

[9] Multitransition homoclinic and heteroclinic solutions of the extended Fisher-Kolmogorov equation [J].

Kalies, WD ;

VanderVorst, RCAM .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 131 (02) :209-228

[10]

KOLMOGOROV A, 1937, B U ETAT MOSCOW, V6, P1

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