Taiwanese Journal of Mathematics

Blow-up for Parabolic Equations and Systems with Nonnegative Potential

Yung-Jen Lin Guo and Masahiko Shimojo

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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.

Article information

Taiwanese J. Math., Volume 15, Number 3 (2011), 995-1005.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 35K05: Heat equation 35K15: Initial value problems for second-order parabolic equations 35K55: Nonlinear parabolic equations 35K61: Nonlinear initial-boundary value problems for nonlinear parabolic equations

blow-up parabolic equation parabolic system


Lin Guo, Yung-Jen; Shimojo, Masahiko. Blow-up for Parabolic Equations and Systems with Nonnegative Potential. Taiwanese J. Math. 15 (2011), no. 3, 995--1005. doi:10.11650/twjm/1500406280. https://projecteuclid.org/euclid.twjm/1500406280

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