Propagation, reflection, and diffraction of singularities of solutions to wave equations

DOI10.1090/S0002-9904-1978-14501-7zbMath0385.35036OpenAlexW2058855910MaRDI QIDQ4165676

Michael E. Taylor

Publication date: 1978

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9904-1978-14501-7

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Scattering theory for PDEs (35P25) Wave equation (35L05) Initial value problems for second-order hyperbolic equations (35L15) Continuation and prolongation of solutions to PDEs (35B60) Initial value problems for PDEs with pseudodifferential operators (35S10)

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Propagation and reflection of singularities for a class of evolution equations ⋮ The Newton polyhedron and oscillatory integral operators ⋮ What is Babinet's principle? ⋮ On the convergence of the time reversal method for thermoacoustic tomography in elastic media ⋮ Guaranteed error bounds on pointwise quantities of interest for transient viscodynamics problems ⋮ Propagation of microlocal singularities for stochastic partial differential equations ⋮ Microlocally accurate solution of the inverse source problem of thermoacoustic tomography ⋮ The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances ⋮ On a mixed initial boundary-value problem of linear elastodynamics ⋮ A trace theorem for solutions of the wave equation, and the remote determination of acoustic sources ⋮ Oscillatory integrals with polynomial phases ⋮ Reflection of singularities of solutions to the wave equation and the leading singularity of the scattering kernel ⋮ The inverse scattering problem for perturbed wave equations ⋮ Tangential cone condition and Lipschitz stability for the full waveform forward operator in the acoustic regime ⋮ Parametrix for the inverse source problem of thermoacoustic tomography with reduced data ⋮ Asymptotic behavior of the spectra of diffraction problems ⋮ Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle

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