Existence of solutions for degenerate parabolic equations with singular terms

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

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