El Hachimi, Abderrahmane; Igbida, Jaouad; Jamea, Ahmed Existence result for nonlinear parabolic problems with \(L^1\)-data. (English) Zbl 1207.35195 Appl. Math. 37, No. 4, 483-508 (2010). The authors study the existence of solutions of the nonlinear parabolic problem \[ \begin{aligned} \frac{\partial u}{\partial t}-\text{div}(|Du-\Theta(u)|^{p-2}(Du-\Theta(u))) +\alpha(u)=&f \quad\;\text{in } ]0, T[\times\Omega,\\ (|Du-\Theta(u)|^{p-2}(Du-\Theta(u)))\cdot \eta + \gamma(u)=&g \quad\;\text{on } ]0, T[\times\partial\Omega, \\ u(0,\cdot )=&u_0 \quad \text{in } \Omega,\end{aligned} \]with initial data in \(L^1\). Such kind of equations describe several physical phenomena such as the filtration of a fluid in a partially satured porous medium and the flow through a porous medium in a turbulent regime The authors use a time discretization of the continuous problem by the Euler forward scheme. Reviewer: Vincenzo Vespri (Firenze) Cited in 4 Documents MSC: 35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations 35K59 Quasilinear parabolic equations Keywords:Euler forward scheme; flow through a porous medium in a turbulent regime PDFBibTeX XMLCite \textit{A. El Hachimi} et al., Appl. Math. 37, No. 4, 483--508 (2010; Zbl 1207.35195) Full Text: DOI