Variable Coefficient Wave Equations and Systems

Part of the Universitext book series (UTX)

Consider, in \({\rm R}_x^n \times {\rm R}_t \), a second order partial differential operator of the form where all coefficients are real and C , and L 1 is a first order operator. We would like L to be an operator similar to the wave operator, and to enjoy the same properties: Finite speed of propagation, energy inequalities, etc. We saw in  Chapter 2 that, for an operator in the plane, it is natural to require that its principal part should be the principal part of a product a real vector fields. Here, suppose first that L is homogeneous (that is, L 1 ≡ 0) with constant coefficients.


Wave Equation Cauchy Problem Geometrical Optic Principal Part Symmetric System 
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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Le Département de MathématiquesUniversité Paris-Sud XIOrsayFrance

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