## 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

### Keywords:

bounds of the blow-up time
Full Text:

### References:

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