The asymptotic stability of viscous shock waves

A viscous shock wave is a traveling wave solution of a system of conservation laws, considered with (partial or total) parabolic regularization (coming, for example, from viscosity, heat conduction, etc). Navier-Stokes equations for a compressible flow or the equations of magnetohydrodynamics are two examples of such systems. In this talk the asymptotic behavior of a perturbation of such a shock will be discussed.