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Full Description
Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the topic, this text is key for researchers and mathematicians specializing in hyperbolic, Schrödinger, Einstein, and partial differential equations; complex analysis; and mathematical physics.
Contents
1. The conference in honor of Jean Vaillant 2. Hyperbolic systems with nondegenerate characteristics 3. The Cauchy problem for hyperbolic operators dominated by the time function 4. A remark on the Cauchy problem for a model hyperbolic operator 5. Gevrey well-posedness of the Cauchy problem for systems 6. Gevrey well-posedness for pseudosymmetric systems with lower order terms 7. Le rôle des fonctions spéciales dans les problèmes de Goursat pour des équations aux dérivés partielles à coefficients constants 8. Influence of the hyperbolic part on decay rates in 1-d thermoelasticity 9. Integration and singularities of solutions for nonlinear second order hyperbolic equation 10. Causal evolution for Einsteinian gravitation 11. On the Cauchy-Kowalevskaya theorem of Nagumo type for systems 12. Differential analysis on stratified spaces 13. Edge Sobolev spaces, weakly hyperbolic equations, and branching of singularities 14. Sur les ondes superficieles de l'eau et le dévelopement de Friedrichs dans le système de coordonnées de Lagrange 15. Problème de Cauchy pour certains systèmes de Leray-Volevich du type de Schrôdinger 16. Systèmes du type de Schrôdinger à raciness caractéristiques multiples 17. Smoothing effect in Gevrey classes for Schrôdinger equations 18. Semiclassical wavefunctions and Schrôdinger equation 19. Strong uniqueness in Gevrey spaces for some elliptic operators 20. A remark on nonuniqueness in the Cauchy problem for elliptic operator having non-Lipschitz coefficients 21. Sur le prolongement analytique de la solution du problème de Cauchy 22. On the projective descriptions of the space of holomorphic germs 23. Microlocal scaling and extension of distributions 24. A lower bound for atomic Hamiltonians and Brownian motion 25. compromised arrow of time
