微分方程式セミナー


2017/5/19(Fri)

16:30--18:00 数学教室 大セミナー室(E301)

吉田 夏海

立命館大学OIC総合研究機構

Asymptotic stability of viscous shock waves to the Cauchy problem for the scalar conservation law with nonlinear flux and viscosity

In this talk, we consider the asymptotic behavior of solutions to the Cauchy problem for the scalar viscous conservation law where the far field states are prescribed. Especially, we deal with the case when the flux function is a non-convex nonlinear function, and also the viscosity is a nonlinear function. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single shock wave, it is proved that the solution of the Cauchy problem tends toward the viscous shock wave as time goes to infinity, provided the initial perturbation is suitably small.