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

收藏

页码：6082 / 6099

页数：18

相关论文

共 50 条

[21] COEXISTENCE AND STABILITY OF SOLUTIONS FOR A CLASS OF REACTION-DIFFUSION SYSTEMS [J].

Zhang, Zhenbu .

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2005,

[22] Stability of Equilibrium Solutions of a Nonlinear Reaction-Diffusion Equation [J].

Hernandez Melo, Cesar Adolfo ;

Demetrio, Luiz Felipe .

BOLETIN DE MATEMATICAS, 2020, 27 (01) :1-14

[23] The existence, uniqueness and stability of positive periodic solution for periodic reaction-diffusion system [J].

Liu Yingdong ;

Li Zhengyuan ;

Ye Qixiao .

Acta Mathematicae Applicatae Sinica, 2001, 17 (1) :1-13

[24] THE EXISTENCE,UNIQUENESS AND STABILITY OF POSITIVE PERIODIC SOLUTION FOR PERIODIC REACTION-DIFFUSION SYSTEM [J].

刘迎东 ;

李正元 ;

叶其孝 .

Acta Mathematicae Applicatae Sinica(English Series), 2001, (01) :1-13

[25] Stability of pyramidal traveling fronts in time-periodic reaction-diffusion equations with degenerate monostable and ignition nonlinearities [J].

Liu, Yuan-Hao ;

Bu, Zhen-Hui ;

Zhang, Suobing .

ADVANCES IN NONLINEAR ANALYSIS, 2025, 14 (01)

[26] MULTIDIMENSIONAL STABILITY OF TIME-PERIODIC PLANAR TRAVELING FRONTS IN BISTABLE REACTION-DIFFUSION EQUATIONS [J].

Sheng, Wei-Jie ;

Li, Wan-Tong .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (05) :2681-2704

[27] STABILITY AND BIFURCATION OF A REACTION-DIFFUSION SYSTEM [J].

HARITI, A ;

CHERRUAULT, Y .

INTERNATIONAL JOURNAL OF BIO-MEDICAL COMPUTING, 1991, 29 (02) :77-94

[28] Convergence of solutions of reaction-diffusion systems with time delays [J].

Pao, CV .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 48 (03) :349-362

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

Bandle, C. ;

Mastrolia, P. ;

Monticelli, D. D. ;

Punzo, F. .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2016, 48 (01) :122-151

[30] Stability of time-dependent diffusion semigroups and kernels [J].

Weian Zheng .

Acta Mathematica Sinica, 1999, 15 :575-586

← 1 2 3 4 5 →