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Stability and convergence of discrete kinetic approximations to an initial-boundary value problem for conservation laws. (English) Zbl 1024.35072

A new convergence result for a semilinear hyperbolic system of the BGK-type to an initial-boundary value problem for scalar hyperbolic conservation law is present. The author shows the stability and convergence results to the unique entropy solution without any restriction on the data. The main novel part of the proof is a careful use of the information along characteristics. Thus there is no need to use the total variation in time to estimate the space total variation along the trace.

MSC:

35L65 Hyperbolic conservation laws
35B45 A priori estimates in context of PDEs
35B25 Singular perturbations in context of PDEs
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