Pointwise estimates and stability for degenerate viscous shock waves Academic Article uri icon

abstract

  • We study the pointwise behavior of perturbed degenerate (sonic) shock waves for scalar conservation laws with constant diffusion. Building on the pointwise Green's function approach of [H1-3], [ZH], we extend the linear analysis to an equation with non-integrable coefficients, arriving at an estimate on linearized perturbations believed sharp to a possible error of size log t. Nonlinear stability for degenerate waves follows in all Lpnorms, p ≧ 1.

author list (cited authors)

  • Howard, P.

publication date

  • December 2002