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2011 Blow-up for Parabolic Equations and Systems with Nonnegative Potential
Yung-Jen Lin Guo, Masahiko Shimojo
Taiwanese J. Math. 15(3): 995-1005 (2011). DOI: 10.11650/twjm/1500406280

Abstract

We study the blow-up behaviors of two parabolic problems on a bounded domain. One is the heat equation with nonlinear memory and the other is a parabolic system with power nonlinearity in which the coefficients of the reaction terms (potentials) are nonnegative and spatially inhomogeneous. Our aim is to show that any zero of the potential, where there is no reaction, is not a blow-up point, if the solution is monotone in time. We also give sufficient conditions for the time monotonicity of solutions.

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Yung-Jen Lin Guo. Masahiko Shimojo. "Blow-up for Parabolic Equations and Systems with Nonnegative Potential." Taiwanese J. Math. 15 (3) 995 - 1005, 2011. https://doi.org/10.11650/twjm/1500406280

Information

Published: 2011
First available in Project Euclid: 18 July 2017

zbMATH: 1235.35049
MathSciNet: MR2829893
Digital Object Identifier: 10.11650/twjm/1500406280

Subjects:
Primary: 35K05 , 35K15 , 35K55 , 35K61

Keywords: Blow-up , parabolic equation , parabolic system

Rights: Copyright © 2011 The Mathematical Society of the Republic of China

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