Une condition nécessaire et suffisante d'existence d'un espace de représentation de H. Bauer

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The Block Structure Condition for Symmetric Hyperbolic Systems

In the analysis of hyperbolic boundary value problems, the constructionof Kreiss' symmetrizers relies on a suitable block structuredecomposition of the symbol of the system. In this paper, weshow that this block structure condition is satisfied by allsymmetrizable hyperbolic systems of constant multiplicity. 2000Mathematics Subject Classification 35L50, 35L67, 35L75.     

A nonlinear instability for 3×3 systems of conservation laws

The phenomenon of nonlinear resonance provides a mechanism for the unbounded amplification of small solutions of systems of conservation laws. We construct spatially 2-periodic solutionsu ^N C ([0,t _N ] × witht _N bounded, satisfying

INVARIANCE AND STABILITY OF THE PROFILE EQUATIONS OF GEOMETRIC OPTICS

The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies for computing profile equations are equivalent. We prove that if L generates an evolution on L 2 the same is true of the profile equations. We prove that the characteristic polynomial of the profile equations is the localization of the characteristic polynomial of the background operator at (y, dφ(y)) where φ is the background phase. We prove that the propagation cones of the profile equations are subsets of the propagation cones of the background operator.