Some existence and regularity results for porous media and fast diffusion equations with a gradient term

Boumediene Abdellaoui, Ireneo Peral, Magdalena Walias

In this paper we consider the problem $$(P)\qquad \{{array}{rclll} u_t-\D u^m&=&|\n u|^q +\,f(x,t),&\quad u\ge 0 \hbox{in} Ω_T\equiv Ω\times (0,T), u(x,t)&=&0 &\quad \hbox{on} \par…