BLOWUP IN A PARTIAL-DIFFERENTIAL EQUATION WITH CONSERVED 1ST INTEGRAL

被引：68

作者：

BUDD, C ^{[1
]}

DOLD, B ^{[1
]}

STUART, A ^{[1
]}

机构：

[1] UNIV BATH,SCH MATH SCI,BATH BA2 7AY,AVON,ENGLAND

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 1993年 / 53卷 / 03期

关键词：

BLOWUP; NONLOCAL SOURCE TERM; CONSERVED INTEGRAL; ADAPTIVE REMESHING;

D O I：

10.1137/0153036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A reaction-diffusion equation with a nonlocal term is studied. The nonlocal term acts to conserve the spatial integral of the unknown function as time evolves. Such equations give insight into biological and chemical problems where conservation properties predominate. The aim of the paper is to understand how the conservation property affects the nature of blowup. The equation studied has a trivial steady solution that is proved to be stable. Existence of nontrivial steady solutions is proved, and their instability established numerically. Blowup is proved for sufficiently large initial data by using a comparison principle in Fourier space. The nature of the blowup is investigated by a combination of asymptotic and numerical calculations.

引用

页码：718 / 742

页数：25

共 22 条

[1] REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NON-LINEAR EVOLUTION EQUATIONS [J].