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Global existence and blow-up phenomena for nonlinear divergence form parabolic equations with inhomogeneous Neumann boundary conditions. (English) Zbl 1227.35157

Summary: We consider nonlinear divergence form parabolic equations with inhomogeneous Neumann boundary conditions. We establish respectively the conditions on nonlinearities to guarantee that \(u(\mathbf x,t)\) exists globally or blows up at some finite time. If blow-up occurs, we obtain upper and lower bounds of the blow-up time.

MSC:

35K51 Initial-boundary value problems for second-order parabolic systems
35B44 Blow-up in context of PDEs
35K58 Semilinear parabolic equations
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