Blow-up phenomena for a class of fourth-order parabolic problems
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Abstract:
This paper deals with some qualitative properties of solutions to a class of semilinear fourth-order parabolic problems. It is shown that under certain conditions on the data, $u(\textbf {x}, t)$ cannot exist for all time and an upper bound for $t^{\star }$ is derived where $(0,t^{\star })$ is the interval of existence of $u(\textbf {x}, t)$. Moreover we construct (under certain conditions on the data) a lower bound for $t^{\star }$ when blow-up occurs. This last result is based on some Sobolev type inequality established at the end of the paper.References
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Additional Information
- G. A. Philippin
- Affiliation: Département de mathématiques et de statistique, Université Laval, Québec, Canada G1V OA6
- Email: gerard.philippin@mat.ulaval.ca
- Received by editor(s): November 20, 2013
- Received by editor(s) in revised form: January 12, 2014
- Published electronically: February 16, 2015
- Communicated by: Michael Hitrik
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 2507-2513
- MSC (2010): Primary 35K30, 35K57
- DOI: https://doi.org/10.1090/S0002-9939-2015-12446-X
- MathSciNet review: 3326032