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| 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}
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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 |
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