On boundedness of solutions of reaction-diffusion equations with nonlinear boundary conditions

Arrieta, José

doi:10.1090/S0002-9939-07-08980-0

On boundedness of solutions of reaction-diffusion equations with nonlinear boundary conditions
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by José M. Arrieta PDF

Proc. Amer. Math. Soc. 136 (2008), 151-160 Request permission

Abstract:

We give conditions on the nonlinearities of a reaction-diffusion equation with nonlinear boundary conditions that guarantee that any solution starting at bounded initial data is bounded locally around a certain point $x_0$ of the boundary, uniformly for all positive time. The conditions imposed are of a local nature and need only to hold in a small neighborhood of the point $x_0$.

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