Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): José M. Arrieta
Journal: Proc. Amer. Math. Soc. 136 (2008), 151-160.
MSC (2000): Primary 35K57, 35B40
Posted: September 27, 2007
MathSciNet review: 2350400
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Abstract | References | Similar articles | Additional information

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 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 .

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