Liu, Dengming; Mu, Chunlai Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition. (English) Zbl 1207.35076 Electron. J. Qual. Theory Differ. Equ. 2010, Paper No. 51, 17 p. (2010). Summary: We consider a semilinear parabolic equation \[ u_t=\Delta u+u^q\int_0^tu^p(x,s)\,ds,\quad x\in \Omega,\;t>0 \]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. Cited in 4 Documents MSC: 35B44 Blow-up in context of PDEs 35B35 Stability in context of PDEs 35K58 Semilinear parabolic equations 35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations Keywords:nonnegative initial data PDFBibTeX XMLCite \textit{D. Liu} and \textit{C. Mu}, Electron. J. Qual. Theory Differ. Equ. 2010, Paper No. 51, 17 p. (2010; Zbl 1207.35076) Full Text: EuDML EMIS