REACTION-DIFFUSION PROBLEMS ON TIME-DEPENDENT RIEMANNIAN MANIFOLDS: STABILITY OF PERIODIC SOLUTIONS

被引：0

作者：

Bandle, C. ^{[1
]}

Monticelli, D. D. ^{[2
]}

Punzo, F. ^{[2
]}

机构：

[1] Univ Basel, CH-4001 Basel, Switzerland

[2] Politecn Milan, I-20133 Milan, Italy

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2018年 / 50卷 / 06期

关键词：

reaction-diffusion equations; stability; instability; Riemannian manifolds; Ricci curvature; EQUATION;

D O I：

10.1137/17M1161865

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the stability of time-periodic solutions of semilinear parabolic problems with Neumann boundary conditions, posed on a domain of a Riemannian manifold. On the domain we consider metrics that vary periodically in time. The discussion is based on the principal eigenvalue of periodic parabolic operators. The study is related to biological models on the effect of growth and curvature on pattern formation. Metric properties, for instance, the Ricci curvature, play a crucial role.

引用

页码：6082 / 6099

页数：18

共 18 条

[1]

Alias L., 2016, Maximum principles and geometric applications

[2]

[Anonymous], PERIODIC SOLUTIONS S

[3] ON THE STABILITY OF SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS ON RIEMANNIAN MANIFOLDS [J].