## Blow-up for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary.(English)Zbl 1276.35041

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

### MSC:

 35B44 Blow-up in context of PDEs 35K58 Semilinear parabolic equations 35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations 35R09 Integro-partial differential equations

### Keywords:

blow-up criteria; blow-up rate
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