The roles of diffusivity and curvature in patterns on surfaces of revolution

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:412

Article

do Nascimento, Arnaldo Simal¹  Sonego, Maicon¹ 

[1] Univ Fed Sao Carlos DM, BR-13565905 Sao Carlos, SP, Brazil

关键词: Patterns;    Curvature;    Diffusivity;    Reaction-diffusion;    Surface of revolution;    Stability;   

DOI  :  10.1016/j.jmaa.2013.10.058

来源: Elsevier

【 摘 要 】

We address the question of finding sufficient conditions for existence as well as nonexistence of nonconstant stable stationary solution to the diffusion equation u(t) = div(a del u) + f(u) on a surface of revolution with and without boundary. Conditions found relate the diffusivity function a and the geometry of the surface where diffusion takes place. In the case where f is a bistable function, necessary conditions for the development of inner transition layers are given. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free