Geodesic
Existence of entropy solutions to nonlinear degenerate parabolic problems with variable exponent and $L^1$-data
Communications in Mathematics, Tome 28 (2020) no. 1, pp. 67-88.

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In the present paper, we prove existence results of entropy solu\-tions to a class of nonlinear degenerate parabolic $p(\cdot )$-Laplacian problem with Dirichlet-type boundary conditions and $L^1$ data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.
Classification : 35A02, 35J60, 35J65, 35J92
Keywords: Degenerate parabolic problem; entropy solution; existence; semi-discretization; Rothe's method; weighted Sobolev space 
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     title = {Existence of entropy solutions to nonlinear degenerate parabolic problems with variable exponent and $L^1$-data},
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Sabri, Abdelali; Jamea, Ahmed; Alaoui, Hamad Talibi. Existence of entropy solutions to nonlinear degenerate parabolic problems with variable exponent and $L^1$-data. Communications in Mathematics, Tome 28 (2020) no. 1, pp. 67-88. http://geodesic.mathdoc.fr/item/COMIM_2020__28_1_a5/