On boundedness of solutions of reaction-diffusion equations with nonlinear boundary conditions
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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 $x_0$.References
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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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 151-160
- MSC (2000): Primary 35K57, 35B40
- DOI: https://doi.org/10.1090/S0002-9939-07-08980-0
- MathSciNet review: 2350400