MULTIDIMENSIONAL STABILITY OF TRAVELING WAVES IN A BISTABLE REACTION-DIFFUSION EQUATION .1.

被引：80

作者：

XIN, JX

机构：

[1] Mathematical Sciences Research Institute, Berkeley, CA 94720

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 1992年 / 17卷 / 11-12期

关键词：

D O I：

10.1080/03605309208820907

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that if the initial condition is a small perturbation of a traveling wave solution of the bistable reaction-diffusion equation in H(m) and L1 (R(n)), m greater-than-or-equal-to n + 1, n greater-than-or-equal-to 4, then the solution of the initial value problem converges to the traveling wave solution in H(m)(R(n)) as t goes to infinity with rate O(t-n-1)/4).

引用

收藏

页码：1889 / 1899

页数：11

相关论文

共 10 条

[1] MULTIDIMENSIONAL NON-LINEAR DIFFUSION ARISING IN POPULATION-GENETICS [J].

ARONSON, DG ;

WEINBERGER, HF .

ADVANCES IN MATHEMATICS, 1978, 30 (01) :33-76

[2] CONVERGENCE TO DIFFUSION WAVES OF SOLUTIONS FOR VISCOUS CONSERVATION-LAWS [J].

CHERN, IL ;

LIU, TP .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1987, 110 (03) :503-517

[3]

FIFE PC, 1977, ARCH RATION MECH AN, V65, P355

[4]

FUJITA H, 1966, J FAC SCI U TOKYO 1, V13, P109

[5]

HENRY D, LECTURE NOTES MATH, V840

[6] ASYMPTOTIC-BEHAVIOR OF A REACTION-DIFFUSION EQUATION IN HIGHER SPACE DIMENSIONS [J].

JONES, CKRT .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1983, 13 (02) :355-364

[7] LARGE-TIME BEHAVIOR OF SOLUTIONS TO HYPERBOLIC PARABOLIC-SYSTEMS OF CONSERVATION-LAWS AND APPLICATIONS [J].

KAWASHIMA, S .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1987, 106 :169-194

[8]

LEVERMORE DC, UNPUB MULTIDIMENSION, V2

[9] STABILITY OF WAVES OF NONLINEAR PARABOLIC-SYSTEMS [J].

SATTINGER, DH .

ADVANCES IN MATHEMATICS, 1976, 22 (03) :312-355

[10] EXISTENCE AND NONEXISTENCE OF GLOBAL-SOLUTIONS FOR A SEMI-LINEAR HEAT-EQUATION [J].

WEISSLER, FB .

ISRAEL JOURNAL OF MATHEMATICS, 1981, 38 (1-2) :29-40