Pointwise Green's function estimates toward stability for multidimensional fourth-order viscous shock fronts |
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Authors: | Peter Howard Changbing Hu |
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Institution: | Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA |
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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. |
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Keywords: | 35P05 35B35 35B40 76L05 |
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