Localization of blow-up points for a nonlinear nonlocal porous medium equation
Localization of blow-up points for a nonlinear nonlocal porous medium equation
This paper deals with the porous medium equation with a nonlinearnonlocal source$u_t=\Delta u^m + au^p\int_\Omega u^q dx,\quad x\in \Omega, t>0$subject to homogeneous Dirichlet condition. We investigate theinfluence of the nonlocal source and local term on blow-upproperties for this system. It is proved that: (i) when $p\leq 1$,the nonlocal source plays …