Complex geometric optics for symmetric hyperbolic systems I: linear theory

Details Complex geometric optics for symmetric hyperbolic systems I: linear theory Complex geometric optics for symmetric hyperbolic systems I: linear theory

2008-02-12

arxiv.org/abs/0802.1691v1

Physics

Mathematical Physics

Scientific paper

We obtain an asymptotic solution for $\ep \to 0$ of the Cauchy problem for linear first-order symmetric hyperbolic systems with oscillatory initial values written in the eikonal form of geometric optics with frequency $1/\ep$, but with complex phases. For the most common linear wave propagation models, this kind on Cauchy problems are well-known in the applied literature and their asymptotic theory, referred to as complex geometric optics, is attracting interest for applications. In this work, which is the first of a series of papers dedicated to complex geometric optics for nonlinear symmetric hyperbolic systems, we develop a rigorous linear theory and set the basis for the subsequent nonlinear analysis.

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