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

Author: José M. Arrieta
Journal: Proc. Amer. Math. Soc. 136 (2008), 151-160
MSC (2000): Primary 35K57, 35B40
Published electronically: September 27, 2007
MathSciNet review: 2350400
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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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José M. Arrieta
Affiliation: Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain

Keywords: Reaction-diffusion, nonlinear boundary conditions, bounded solutions, blow-up
Received by editor(s): December 9, 2005
Received by editor(s) in revised form: September 19, 2006
Published electronically: September 27, 2007
Additional Notes: The author was partially supported by DGES, BFM2003-03810 DGES, Spain.
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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