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A discrete BGK approximation for strongly degenerate parabolic problems with boundary conditions |
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| Authors: | FR Guarguaglini V Miliši? |
| Institution: | a Dipartimento di Matematica Pura e Applicata, Universitá degli Studi di L'Aquila, Via Vetoio, Coppito I-67100 (L'Aquila), Italy b Modelling and Scientific Computing Chair, Ecole Polytechnique Fédérale de Lausanne, SB/IACS/CMCS, 1015 Lausanne, Switzerland c Dipartimento di Matematica Universitá di Roma “La Sapienza”, Piazzale Aldo Moro n. 5, Roma I-00185, Italy |
| Abstract: | We consider a class of BGK systems with a finite number of velocities, depending on a positive relaxation parameter, that approximate strongly degenerate hyperbolic-parabolic equations with initial boundary conditions. We prove a priori estimates for the solutions of the systems, showing that these functions converge towards the entropy solutions of strongly degenerate problems when the relaxation parameter goes to zero. |
| Keywords: | Entropy solutions Strongly degenerate parabolic equations Singular perturbation problems BGK models |
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