Asymptotic stability of Riemann solutions in BGK approximations to certain multidimensional systems of conservation laws |
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Authors: | Hermano Frid,Leonardo Rendó n |
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Affiliation: | a Instituto de Matemática Pura e Aplicada—IMPA, Estrada Dona Castorina, 110, Rio de Janeiro, RJ 22460-320, Brazil b Ciudad Universitaria, Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia |
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Abstract: | 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→∞ in of the space of directions ζ=x/t. That is, the solution z(t,x,ξ) of the perturbed Cauchy problem for the corresponding BGK system satisfies as t→∞, in , where R(ζ) is the self-similar entropy solution of the two-states nonplanar Riemann problem for the system of conservation laws. |
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Keywords: | primary, 35B40, 35B35 secondary, 35L65, 35K55 |
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