Pointwise Green's function estimates toward stability for multidimensional fourth order viscous shock fronts

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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.

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