Blow-up problem for nonlinear nonlocal parabolic equation with absorption under nonlinear nonlocal boundary condition

In this paper we consider initial boundary value problem for nonlinear nonlocal parabolic equation with absorption under nonlinear nonlocal boundary condition and nonnegative initial datum. We prove comparison principle, global existence and blow-up of solutions.Comment: arXiv admin note: text overlap with arXiv:1602.0501

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

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 $u|_{\partial\Omega\times(0,+\infty)}=\int_\Omega\varphi(x,y) u^l(y,t)dy$ and nonnegative initial data, where $p$, $q\geq 0$ and $l>0$. The blow-up criteria and the blow-up rate are obtained