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.
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机译：在本文中，我们处理的抛物线问题的最简单模型是$$ \ begin {cases} u'- \ Delta_ {p} u + B \ frac {| \ nabla u | ^ p} {u} = 0＆\ text { in}（0，T）\ times \ Omega，\ newline u（0，x）= u_0（x）＆\ text {in} \ \ Omega，\ newline u（t，x）= 0＆\ text {on} \（0，T）\ times \ partial \ Omega，\ end {cases} $$，其中$ T> 0 $，$ N \ geq 2 $，$ p> 1 $，$ B> 0 $和$ u_ { 0} $是$ L ^ {\ infty}（\ Omega）$远离零的正函数。
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