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).

报告人简介：Yury Trakhinin，俄罗斯科学院通讯院士，俄罗斯科学院Sobolev数学研究所首席研究员、国际数学中心主任，1994年在新西伯利亚国立大学获得博士学位，2006年获得俄罗斯科学博士学位。Trakhinin教授长期从事流体力学中的非线性偏微分方程的数学研究，近期主要研究兴趣为流体力学中非线性偏微分方程的自由边界问题。研究成果发表于Comm. Pure Appl. Math.、Arch. Ration. Mech. Anal.、Comm. Math. Phys.、Math. Ann.等学术期刊。