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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 $\Omega\times \bbfR^+$ with given initial data and nonlocal boundary condition of the form $Bu(x,t)=$ \break $\int_\Omega K(x,y)u(t,y)dy$, where $Bu= \alpha_0\partial u/\partial\nu+ u$ and $\alpha_0\ge 0$ (nonlocal Dirichlet or Robin condition). Under suitable assumptions on $K$ and the nonlinearity the solution displays corresponding asymptotic behavior. For $K\ge 0$ and $\widehat K(x)= \int_\Omega K(x,y)dy\ge 1$, for instance, the solution can blow up in finite time.
Reviewer: B.Kawohl (Köln)

35B40Asymptotic behavior of solutions of PDE
35K20Second order parabolic equations, initial boundary value problems
35K57Reaction-diffusion equations
Full Text: DOI
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