Kreiss Symmetrizers and Mutidimensional Stability of Shock Profiles
speaker: Guy Métivier (IMB Université de Bordeaux - CNRS)abstract: This course is an introduction to a series of papers by O.Guès, M.Williams, K.Zumbrun and the lecturer, about the stability analysis of nonlinear multidimensional boundary layers and shock waves, emphasizing the construction of symmetrizers used to prove maximal energy estimates. The first part is devoted to boundary value problems for hyperbolic systems, reviewing classical materials with a few new improvements : plane wave analysis, Lopatinski determinant, the method of symmetrizers, Kreiss' construction of symmetrizers, the block structure condition. In the second part, we give an extension of the previous notions to hyperbolic-parabolic systems, that is viscous perturbations of hyperbolic equations. The third part is devoted to a short introduction to applications to boundary layers: profiles equations, the plane wave analysis, introduction of the Evans function, the conjugation lemma, symmetrizers and adapted paradifferential calculi.
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