Time-asymptotic behavior of wave propagation around a viscous shock profile
The authors study the nonlinear stability of viscous shock waves for the system of viscous conservation laws \(u_t+f(u)_x=u_{xx}\). Using a new construction of a fundamental solution for a linearized system around a shock profile, they obtain, for the first time, a pointwise estimate of nonlinear wave interaction across a shock wave. Since these results apply to all ranges of weak shock waves and small perturbations, they reduce to the time-asymptotic behavior of a constant state perturbation, uniformly as the strength of the shock wave tends to zero.
scientific article; zbMATH DE number 5655471