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Bifurcation points for a reaction-diffusion system with two inequalities. (English) Zbl 1185.35074
Summary: We consider a reaction-diffusion system of activator-inhibitor or substrate-depletion type which is subject to diffusion-driven instability. We show that obstacles (e.g., a unilateral membrane) for both quantities modeled in terms of inequalities introduce a new bifurcation of spatially non-homogeneous steady states in the domain of stability of the trivial solution of the corresponding classical problem without obstacles.

MSC:
35J57 Boundary value problems for second-order elliptic systems
35P05 General topics in linear spectral theory for PDEs
35B32 Bifurcations in context of PDEs
35J50 Variational methods for elliptic systems
49J40 Variational inequalities
35B35 Stability in context of PDEs
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