In this paper we deal with parabolic problems whose simplest model is $$ \begin{ cases} u'- \Delta_{ p} u + B\frac{ |\nabla u|^p}{ u} = 0 & \text{ in} (0,T) \times \Omega,\newline u(0,x)= u_0 (x) &\text{ in}\ \Omega, \newline u(t,x)=0 &\text{ on}\ (0,T) \times \partial\Omega, \end{ cases} $$ where $T>0$, $N\geq 2$, $p>1$, $B > 0$, and $u_{ 0}$ is a positive function in $L^{ \infty}(\Omega)$ bounded away from zero.
Categories: math.AP