Asymptotic behavior of the solutions of the dead-core problem. (English) Zbl 0699.35022

The authors treat the problem of determining the asymptotic behavior of solutions to nonlinear degenerate parabolic initial boundary value problems by constructing appropriate sub- and supersolutions. The authors obtain these solutions by using similarity transformation methods for stationary solutions. The results are applied to the ‘dead-core’ problem in reaction-diffusion processes; this means that the existence of stationary solutions with compact support can be proved.
Reviewer: H.Lange


35B40 Asymptotic behavior of solutions to PDEs
35K57 Reaction-diffusion equations
35K20 Initial-boundary value problems for second-order parabolic equations
35A30 Geometric theory, characteristics, transformations in context of PDEs
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