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.