Stochastic perturbations method for a system of Riemann invariants

zbMATH Open1327.35466arXiv1310.7147MaRDI QIDQ5175508

Olga S. Rozanova

Publication date: 23 February 2015

Abstract: Basing on our results [1] on a representation of solutions to the Cauchy problem for multidimensional non-viscous Burgers equation obtained by a method of stochastic perturbation of the associated Langevin system, we deduce an explicit asymptotic formula for smooth solutions to the Cauchy problem for any genuinely nonlinear hyperbolic system of equations written in the Riemann invariants.

Full work available at URL: https://arxiv.org/abs/1310.7147

zbMATH Keywords

Cauchy problemRiemann invariantsstochastic perturbationrepresentation of solutionassociated conservation laws

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) PDEs in connection with fluid mechanics (35Q35) Hyperbolic conservation laws (35L65) PDEs with randomness, stochastic partial differential equations (35R60)

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