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Eigenvalues of inequalities of reaction-diffusion type and destabilizing effect of unilateral conditions. (English) Zbl 0608.35032

The linearized stability of the reaction-diffusion system \[ \partial u/\partial t=d\Delta u+f(u,v);\quad \partial v/\partial t=\Delta v+g(u,v) \] with unilateral boundary conditions \(\partial v/\partial n\geq 0\), \(v\geq 0\) on part of the boundary are considered. In particular it is shown that the unilateral conditions have a destabilizing effect, compared with the corresponding bilateral conditions. This is achieved by writing the system as a variational inequality in the abstract Lions formulation.
Reviewer: S.Banks

MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B35 Stability in context of PDEs
35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
35P05 General topics in linear spectral theory for PDEs
35K57 Reaction-diffusion equations
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References:

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