In this article, we investigate the interaction between two regularizing terms in the following parabolic problem \(\begin{aligned} \left\{ \begin{array}{ll} \dfrac{\partial u}{\partial t}-\Delta u+\dfrac{\vert \nabla u\vert ^{2}}{u^{\theta }}=\dfrac{f}{u^{\gamma }}& \text{ in }\ Q, \\ u(x,t)=0& \text{ on }\, \Gamma , \\ u(x,0)=u_{0}(x)& \text{ in }\, \Omega , \end{array}\right. \end{aligned}\) where \(\Omega \subset \mathbb {R}^{N}\) ( \(N\ge 3\) ) is an open bounded set with boundary \(\partial \Omega \) , \(Q=\Omega \times (0, T)\) , \(0< T < +\infty \) , \(\Gamma =\partial \Omega \times (0, T)\) , \(0<\theta <1\) , \(0<\gamma \le 1\) , \(f\in L^{m}(Q)\) , \(1\le m<\frac{N}{2}+1\) , and \(u_{0}\in L^{\infty }(\Omega )\) such that \(\begin{aligned} \forall \omega \subset \subset \Omega ,~\exists d_{\omega }>0:~u_{0}\ge d_{\omega }~\text{ in }~\omega . \end{aligned}\) The aim of the paper is to extend the results recently obtained in [2] for the associated singular stationary problem.
