Geodesic
Instability of Turing type for a reaction-diffusion system with unilateral obstacles modeled by variational inequalities
Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 195-211.

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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.
DOI : 10.21136/MB.2014.143849
Classification : 34D20, 35B35, 35K51, 35K57, 35K86, 35K87, 47H05, 47H11, 47J20, 47J35
Keywords: reaction-diffusion system; Signorini condition; unilateral obstacle; instability; asymptotic stability; parabolic obstacle equation 
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Väth, Martin. Instability of Turing type for a reaction-diffusion system with unilateral obstacles modeled by variational inequalities. Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 195-211. doi : 10.21136/MB.2014.143849. http://geodesic.mathdoc.fr/articles/10.21136/MB.2014.143849/

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