Instability of Turing type for a reaction-diffusion system with unilateral obstacles modeled by variational inequalities

Title:

Instability of Turing type for a reaction-diffusion system with unilateral obstacles modeled by variational inequalities

Creator:

Väth, Martin

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:04b83462-73a3-4b5c-90c4-2ca2b98bda77
uuid:04b83462-73a3-4b5c-90c4-2ca2b98bda77
doi:10.21136/MB.2014.143849

Subject:

reaction-diffusion system, Signorini condition, unilateral obstacle, instability, asymptotic stability, and parabolic obstacle equation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We consider a reaction-diffusion system of activator-inhibitor type which is subject to Turing's diffusion-driven instability. It is shown that unilateral obstacles of various type for the inhibitor, modeled by variational inequalities, lead to instability of the trivial solution in a parameter domain where it would be stable otherwise. The result is based on a previous joint work with I.-S. Kim, but a refinement of the underlying theoretical tool is developed. Moreover, a different regime of parameters is considered for which instability is shown also when there are simultaneously obstacles for the activator and inhibitor, obstacles of opposite direction for the inhibitor, or in the presence of Dirichlet conditions.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

195-211

Source:

Mathematica bohemica | 2014 Volume:139 | Number:2

Harvested from:

CDK

Metadata only:

false