Display Abstract

Title Problems with singularity in the u variable: nonnegative solutions

Name Daniela D Giachetti
Country Italy
Email daniela.giachetti@sbai.uniroma1.it
Co-Author(s) Daniela Giachetti
Submit Time 2014-04-09 10:18:46
Special Session 37: Global or/and blowup solutions for nonlinear evolution equations and their applications
We deal with the existence of nonnegative solutions to parabolic problems which are singular in the $u$ variable whose model is \begin{displaymath} \left\{ \begin{array}{ll} u_t-\Delta_p u=f(x,t)(\frac{1}{u^\theta}+1) & \textrm{in $\Omega\times(0,T)$}\\ u(x,t)=0 & \textrm{on $\partial\Omega\times(0,T)$}\\ u(x,0)=u_0(x) & \textrm{in $\Omega$.} \end{array} \right. \end{displaymath} \\ Here $\Omega$ is a bounded open subset of $\mathbb{R}^N, N\geq 2,\, 01$.\\ As far as the data, we assume $f(x,t)\in L^r(0,T;L^m(\Omega))$, with $\frac{1}{r}+\frac{N}{pm}0$, $D>0$, $1