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Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions. (English) Zbl 0920.35030
The author investigates the asymptotic behavior of solutions to a semilinear parabolic equation on Ω× + with given initial data and nonlocal boundary condition of the form Bu(x,t)= Ω K(x,y)u(t,y)dy, where Bu=α 0 u/ν+u and α 0 0 (nonlocal Dirichlet or Robin condition). Under suitable assumptions on K and the nonlinearity the solution displays corresponding asymptotic behavior. For K0 and K ^(x)= Ω K(x,y)dy1, for instance, the solution can blow up in finite time.
Reviewer: B.Kawohl (Köln)
MSC:
35B40Asymptotic behavior of solutions of PDE
35K20Second order parabolic equations, initial boundary value problems
35K57Reaction-diffusion equations