Asymptotic stability of Riemann solutions in BGK approximations to certain multidimensional systems of conservation laws

[摘要] We prove the asymptotic stability of nonplanar two-states Riemann solutions in BGK approximations of a class of multidimensional systems of conservation laws. The latter consists of systems whose flux-functions in different directions share a common complete system of Riemann invariants, the level surfaces of which are hyperplanes. The asymptotic stability to which the main result refers is in the sense of the convergence as t -> infinity in L-loc(1) of the space of directions zeta = x/t. That is, the solution z(t, x,xi) of the perturbed Cauchy problem for the corresponding BGK system satisfies integral(X) z(t, t zeta, xi) d mu(xi) -> R(zeta) as t -> infinity, in L-loc(1)(R-n), where R(zeta) is the self-similar entropy solution of the two-states nonplanar Riemann problem for the system of conservation laws. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-11-15

[关键词] conservation laws;BGK approximations;Riemann problems;asymptotic stability;multidimensional systems