Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition

Dengming Liu, Chongqing University, Chongqing, P. R. China
Chunlai Mu, Chongqing University, Chongqing, P. R. China

E. J. Qualitative Theory of Diff. Equ., No. 51. (2010), pp. 1-17.

Abstract: In this paper, we consider a semilinear parabolic equation
$$u_t=\Delta u+u^q\int_0^tu^p(x,s)ds,\quad x\in \Omega,\quad t>0$$
with nonlocal nonlinear boundary condition $u|_{\partial\Omega\times(0,+\infty)}=\int_\Omeg\varphi(x,y) u^l(y,t)dy$ and nonnegative initial data, where $p$, $q\geq 0$ and $l>0$. The blow-up criteria and the blow-up rate are obtained.

You can download the full text of this paper in DVI, PostScript or PDF format.