An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle

被引：11

作者：

Fiedler, B. ^{[1
]}

Grotta-Ragazzo, C. ^{[2
]}

Rocha, C. ^{[3
]}

机构：

[1] Free Univ Berlin, Inst Math, Berlin, Germany

[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, Brazil

[3] Inst Super Tecn, Lisbon, Portugal

来源：

RUSSIAN MATHEMATICAL SURVEYS | 2014年 / 69卷 / 03期

关键词：

partial differential equations; variational methods; convection; energy functional; advection; reaction-diffusion equations; periodic boundary conditions; ROTATING WAVES; DYNAMICS;

D O I：

10.1070/RM2014v069n03ABEH004897

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An explicit Lyapunov function is constructed for scalar parabolic reaction-advection-diffusion equations under periodic boundary conditions. The non-linearity is assumed to be even with respect to the advection term. The method followed was originally suggested by H. Matano for, and limited to, separated boundary conditions.

引用

页码：419 / 433

页数：15

共 20 条

[1] THE ZERO-SET OF A SOLUTION OF A PARABOLIC EQUATION [J].