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A multi-scale Gaussian beam parametrix for the wave equation: the Dirichlet boundary value problem. (English) Zbl 1480.35027

Summary: We present a construction of a multi-scale Gaussian beam parametrix for the Dirichlet boundary value problem associated with the wave equation, and study its convergence rate to the true solution in the highly oscillatory regime. The construction elaborates on the wave-atom parametrix of Bao, Qian, Ying, and Zhang and extends to a multi-scale setting the technique of Gaussian beam propagation from a boundary of Katchalov, Kurylev and Lassas.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35C10 Series solutions to PDEs
35L05 Wave equation
35L20 Initial-boundary value problems for second-order hyperbolic equations
35S05 Pseudodifferential operators as generalizations of partial differential operators
42C15 General harmonic expansions, frames
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