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Transactions of the American Mathematical Society

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Blow-up of solutions of nonlinear parabolic inequalities


Author: Steven D. Taliaferro
Journal: Trans. Amer. Math. Soc. 361 (2009), 3289-3302
MSC (2000): Primary 35K55, 35B40, 35R45
DOI: https://doi.org/10.1090/S0002-9947-09-04770-9
Published electronically: January 26, 2009
MathSciNet review: 2485427
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Abstract | References | Similar Articles | Additional Information

Abstract: We study nonnegative solutions $ u(x,t)$ of the nonlinear parabolic inequalities

$\displaystyle au^\lambda \le u_t - \Delta u \le u^\lambda $

in various subsets of $ {\bf R}^n\times {\bf R}$, where $ \lambda>\frac{n+2}{n}$ and $ a\in (0,1)$ are constants. We show that changing the value of $ a$ in the open interval $ (0,1)$ can dramatically affect the blow-up of these solutions.


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Additional Information

Steven D. Taliaferro
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: stalia@math.tamu.edu

DOI: https://doi.org/10.1090/S0002-9947-09-04770-9
Received by editor(s): September 4, 2007
Published electronically: January 26, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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