On a nonlinear elliptic-parabolic integro-differential equation with L-data |
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Authors: | Volker G Jakubowski |
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Institution: | a Fachbereich Mathematik, Universität Duisburg-Essen, D-45117 Essen, Germany b UFR de Mathématiques, Université Louis Pasteur, F-67084 Strasbourg, France |
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Abstract: | We generalize the concept of entropy solutions for parabolic equations with L1-data and consider a class of nonlinear history-dependent degenerated elliptic-parabolic equations including problems with a fractional time derivative such as with Dirichlet boundary conditions and initial condition, where 0<γ?1. We show uniqueness of entropy solutions for general L1-data by Kruzhkov's method of doubling variables. Moreover, existence in the nondegenerated case, i.e. b≡id, is shown by using the concept of generalized solutions of a corresponding abstract Volterra equation. |
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Keywords: | Nonlinear elliptic-parabolic equations Fractional time derivative L1 data |
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