Abstract
In this paper we study the hydrodynamic limit of a B.G.K. like kinetic model on domains with boundaries via BV loc theory. We obtain as a consequence existence results for scalar multidimensional conservation laws with kinetic boundary conditions. We require that the initial and boundary data satisfy the optimal assumptions that they all belong to L 1∩L ∞ with the additional regularity assumptions that the initial data are in BV loc . We also extend our hydrodynamic limit analysis to the case of a generalized kinetic model to account for forces effects and we obtain as a consequence the existence theory for conservation laws with source terms and kinetic boundary conditions.
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M. Tidriri, Analysis of a coupled system of kinetic equations and their hydrodynamic (conservation laws) limit: Rigorous derivation and existence theory via BV theory. Preprint.
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M. Tidriri, Hydrodynamic limit of a BGK kinetic model and kinetic formulation of conservation laws on domains with boundaries. Preprint.
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Tidriri, M. Hydrodynamic Limit of a B.G.K. Like Model on Domains with Boundaries and Analysis of Kinetic Boundary Conditions for Scalar Multidimensional Conservation Laws. Journal of Statistical Physics 115, 1715–1754 (2004). https://doi.org/10.1023/B:JOSS.0000028079.51072.06
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DOI: https://doi.org/10.1023/B:JOSS.0000028079.51072.06