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Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p ( x )-Laplacian with Neumann Boundary Condition
Laboratoire de Mathématiques Fondamentales et Applications (LMFA), Département de Mathématiques, École Normale Supérieure, Université Abdou Moumouni de Niamey, Niamey, Niger
Laboratoire Interdisciplinaire de Recherche en Sciences Appliquées (LIRSA), École Normale Supérieure, Burkina Faso
- 1 Laboratoire de Mathématiques Fondamentales et Applications (LMFA), Département de Mathématiques, École Normale Supérieure, Université Abdou Moumouni de Niamey, Niamey, Niger
- 2 Laboratoire Interdisciplinaire de Recherche en Sciences Appliquées (LIRSA), École Normale Supérieure, Burkina Faso
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Abstract
We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p ( x )-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
KeywordsLebesgue and Sobolev Spaces with Variable ExponentWeak SolutionEntropy SolutionDegenerate Parabolic-Hyperbolic EquationConservation LawLeray Lions Type OperatorNeumann Boundary ConditionExistence Result
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