Time-asymptotic behavior of wave propagation around a viscous shock profile

Academic Article


  • We study the nonlinear stability of shock waves for viscous conservation laws. Our approach is based on a new construction of a fundamental solution for a linearized system around a shock profile. We obtain, for the first time, the pointwise estimates of nonlinear wave interactions across a shock wave. Our results apply to all ranges of weak shock waves and small perturbations. In particular, our results reduce to the time-asymptotic behavior of constant state perturbation, uniformly as the strength of the shock wave tends to zero. © Springer-Verlag 2009.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Liu TP; Zeng Y
  • Start Page

  • 23
  • End Page

  • 82
  • Volume

  • 290
  • Issue

  • 1