Nonlinear parabolic problems with Neumann-type boundary conditions and L^1-data

A. El Hachimi, University Chouaib Doukkali, El Jadida, Maroc
A. Jamea, University Chouaib Doukkali, El Jadida, Maroc

E. J. Qualitative Theory of Diff. Equ., No. 27. (2007), pp. 1-22.

Abstract: In this paper, we study existence, uniqueness and stability questions for the nonlinear parabolic equation:
$$ \frac{\partial u}{\partial t}-\triangle_{p}u+\alpha(u)=f in ]0,\ T[\times\Omega, $$ with Neumann-type boundary conditions and initial data in $L^1$. Our approach is based essentially on the time discretization technique by Euler forward scheme.

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