## Taiwanese Journal of Mathematics

### BLOW-UP FOR A SEMILINEAR PARABOLIC EQUATION WITH NONLINEAR MEMORY AND NONLOCAL NONLINEAR BOUNDARY

#### 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.

#### Article information

Source
Taiwanese J. Math., Volume 17, Number 4 (2013), 1353-1370.

Dates
First available in Project Euclid: 10 July 2017

https://projecteuclid.org/euclid.twjm/1499706121

Digital Object Identifier
doi:10.11650/tjm.17.2013.2648

Mathematical Reviews number (MathSciNet)
MR3085515

Zentralblatt MATH identifier
1276.35041

Subjects
Primary: 35B35: Stability 35K50 35K55: Nonlinear parabolic equations

#### Citation

Liu, Dengming; Mu, Chunlai; Ahmed, Iftikhar. BLOW-UP FOR A SEMILINEAR PARABOLIC EQUATION WITH NONLINEAR MEMORY AND NONLOCAL NONLINEAR BOUNDARY. Taiwanese J. Math. 17 (2013), no. 4, 1353--1370. doi:10.11650/tjm.17.2013.2648. https://projecteuclid.org/euclid.twjm/1499706121

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