Pointwise Green's function estimates toward stability for multidimensional fourth-order viscous shock fronts Academic Article uri icon

abstract

  • For the case of multidimensional viscous conservation laws with fourth-order smoothing only, we develop detailed pointwise estimates on the Green's function for the linear fourth-order convection equation that arises upon linearization of the conservation law about a viscous planar wave solution. As in previous analyses in the case of second-order smoothing, our estimates are sufficient to establish that spectral stability implies nonlinear stability, though the full development of this result will be considered in a companion paper. © 2005 Elsevier Inc. All rights reserved.

author list (cited authors)

  • Howard, P., & Hu, C.

citation count

  • 4

publication date

  • November 2005