#### Hichem Khelifi, Some regularity of nonlinear degenerate parabolic equations with $L^1$ data, Vol. 2021 (2021), Article ID 11, pp. 1-13

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DOI: 10.23952/cot.2021.11

Received July 29, 2020; Accepted October 9, 2021; Published October 24, 2021

Abstract. In this paper, we prove the existence of solutions of nonlinear anisotropic parabolic equations whose model is $\frac{\partial u}{\partial t}-\mbox{div}\left(\frac{\vert u\vert^{p-2}\nabla u}{(1+\vert u\vert)^{\gamma}}\right)=f,$ on $\Omega\times (0,T),$ with homogeneous Cauchy-Dirichlet boundary conditions, where $\gamma+1, $0\leq \gamma <1$, and $f$ belongs to $L^1$.

Hichem Khelifi, Some regularity of nonlinear degenerate parabolic equations with $L^1$ data, Communications in Optimization Theory, Vol. 2021 (2021), Article ID 11, pp. 1-13.