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Multidimensional viscous shocks I: Degenerate symmetrizers and long time stability |
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| Authors: | Olivier Guè s Guy Mé tivier Mark Williams Kevin Zumbrun |
| Affiliation: | LATP, Université de Provence, 39 rue Joliot-Curie, 13453 Marseille, France ; MAB, Université de Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, France ; University of North Carolina, Department of Mathematics, CB 3250, Phillips Hall, Chapel Hill, NC 27599 ; Indiana University, Department of Mathematics, Rawles Hall, Bloomington, IN 47405 |
| Abstract: | We use energy estimates to study the long time stability of multidimensional planar viscous shocks  for systems of conservation laws. Stability is proved for both zero mass and nonzero mass perturbations, and some of the results include rates of decay in time. Shocks of any strength are allowed, subject to an appropriate Evans function condition. The main tools are a conjugation argument that allows us to replace the eigenvalue equation by a problem in which the  dependence of the coefficients is removed and degenerate Kreiss-type symmetrizers designed to cope with the vanishing of the Evans function for zero frequency. |
| Keywords: | Viscous shock stability Evans-Lopatinski condition Kreiss symmetrizers |
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