Speaker : | Olga Rozanova (Moscow State University) |
Title : | Balance laws related to a stochastic representation of solutions to systems of quasilinear equations |
Time : | 2017-08-01 (Tue) 10:30 - 11:30 |
Place : | Auditorium, 6 Floor, Institute of Mathematics (NTU Campus) |
Abstract: | We show that an asymptotic representation of smooth solutions to the Cauchy problem for any genuinely nonlinear hyperbolic system of equations written in the Riemann invariants can be obtained by a method of stochastic perturbation of the associated Langevin system. On this way we associate with the stochastically perturbed equations a system of viscous balance laws. Till the moment of the shock formation the above system of viscous balance laws can be reduced to the pressureless gas dynamics system (in a limit as the parameters of perturbation tend to zero). If the solution to the initial system contains shocks, the limit system is equivalent to the system with a specific pressure, in some sense analogous to the pressure of barotropic monoatomic gas. Based on the solution of this auxiliary system we give a definition of a generalized solution of the initial hyperbolic system in the sense of "free particles". |