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

Liu, Dengming; Mu, Chunlai; Ahmed, Iftikhar

Taiwanese J. Math. 17, No. 4, 1353-1370 (2013).

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	Integral partial differential equations

Keywords:

blow-up criteria; blow-up rate