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In this paper we study the hydrodynamic limit of a B.G.K. like kinetic modelon domains with boundaries via $BV_{loc}$ theory. We obtain as a consequenceexistence results for scalar multidimensional conservation laws with kineticboundary conditions. We require that the initial and boundary data satisfy theoptimal assumptions that they all belong to $L^1\cap L^\infty$ with theadditional regularity assumptions that the initial data are in $BV_{loc}$. Wealso extend our hydrodynamic analysis to the case of a generalized kineticmodel to account for forces effects and we obtain as a consequence theexistence theory for conservation laws with source terms and kinetic boundaryconditions

journal of statistical physics

Hydrodynamic Limit of a B.G.K. Like Model on Domains with Boundaries and Analysis of Kinetic Boundary Conditions for Scalar Multidimensional Conservation Laws