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Blow-up problem for semilinear heat equation with nonlinear nonlocal Neumann boundary condition

This work is supported by the state program of fundamental research of Belarus, grant 1.2.03.1

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  • In this paper, we consider a semilinear parabolic equation with nonlinear nonlocal Neumann boundary condition and nonnegative initial datum. We first prove global existence result. We then give some criteria on this problem which determine whether the solutions blow up in finite time for large or for all nontrivial initial data. Finally, we show that under certain conditions blow-up occurs only on the boundary.

    Mathematics Subject Classification: Primary: 35B44, 35K58, 35K61.

    Citation:

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