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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

José M. Arrieta
Affiliation: Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
Email: arrieta@mat.ucm.es

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08980-0
PII: S 0002-9939(07)08980-0
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.