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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
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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  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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Additional Information:
José
M.
Arrieta
Affiliation:
Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
Email:
arrieta@mat.ucm.es
DOI:
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
Posted:
September 27, 2007
Additional Notes:
The author was partially supported by DGES, BFM2003-03810 DGES, Spain.
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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