We discuss results on the structural stability of shock waves in elastodynamics describing the isentropic motion of compressible neo-Hooken materials. By nonlinear structural stability of a shock wave we mean the local-in-time existence and uniqueness of the discontinuous shock front solution to the corresponding system of hyperbolic conservation laws. We describe finding 2D and 3D structural stability conditions. We also briefly discuss difficulties of the stability analysis for shock waves in nonisentropic elastodynamics (thermoelasticity).

Speaker Biography:

Yury Trakhinin, a corresponding member of the Russian Academy of Sciences, is the chief researcher of the Sobolev Institute of Mathematics of the Russian Academy of Sciences and the director of the International Center for Mathematics. He received his Ph.D. from Novosibirsk State University in 1994 and his Ph.D. in Science from Russia in 2006. Professor Trakhinin has long been engaged in the mathematical research of nonlinear partial differential equations in fluid mechanics. His recent main research interest lies in the free boundary problem of nonlinear partial differential equations in fluid mechanics. The research results were published in Comm. Pure Appl. Math., Arch. Ration. Mech. Anal., Comm. Math. Phys., Math. Ann. Such as academic journals.