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2013 BLOW-UP FOR A SEMILINEAR PARABOLIC EQUATION WITH NONLINEAR MEMORY AND NONLOCAL NONLINEAR BOUNDARY
Dengming Liu, Chunlai Mu, Iftikhar Ahmed
Taiwanese J. Math. 17(4): 1353-1370 (2013). DOI: 10.11650/tjm.17.2013.2648

Abstract

In this paper, we study a semilinear parabolic equation $$u_t = \Delta u + \int_0^t u^p ds - ku^q, \quad x \in \Omega ,\quad t\gt 0$$ with boundary condition $u(x,t) = \int_\Omega f(x,y) u^l(y,t) dy$ for $x \in \partial\Omega$, $t \gt 0$, where $p$, $q$, $l$, $k\gt 0$. The blow-up criteria and the blow-up rate are obtained under some appropriate assumptions.

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Dengming Liu. Chunlai Mu. Iftikhar Ahmed. "BLOW-UP FOR A SEMILINEAR PARABOLIC EQUATION WITH NONLINEAR MEMORY AND NONLOCAL NONLINEAR BOUNDARY." Taiwanese J. Math. 17 (4) 1353 - 1370, 2013. https://doi.org/10.11650/tjm.17.2013.2648

Information

Published: 2013
First available in Project Euclid: 10 July 2017

MathSciNet: MR3085515
zbMATH: 1276.35041
Digital Object Identifier: 10.11650/tjm.17.2013.2648

Subjects:
Primary: 35B35, 35K50, 35K55

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 4 • 2013
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