Georgia Institute of Technology College of Sciences

Shock waves are idealizations of steep spatial gradients of physical quantities such as pressure and density in a gas, or stress in an elastic solid. In this talk, I outline the mathematics of shock waves for nonlinear partial differential equations that are simple models of physical systems. I will focus on non-classical shocks and smooth waves that they approximate. Of particular interest are comparisons between nonlinear traveling waves influenced strongly by dissipative effects such as viscosity or surface tension, and spreading waves generated by the balance between dispersion and nonlinearity, when the nonlinearity is non-convex.