Factorization of the dissipative wave equation and inverse scattering

DOI10.1063/1.528150zbMath0665.35042OpenAlexW1991549627MaRDI QIDQ3816429

Vaughan H. Weston

Publication date: 1988

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.528150

zbMATH Keywords

inverse problemdecompositionfactorizationscattered fielddissipative wave equationreflection operatorreflection kernelsmooth surfaceRiccati integral-differential equation

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Partial differential equations of mathematical physics and other areas of application (35Q99) Second-order hyperbolic equations (35L10)

Related Items (9)

Wave splitting and the reflection operator for the wave equation in R3 ⋮ Determination of the permittivity and conductivity in R3 using wave splitting of Maxwell’s equations ⋮ Erratum: Factorization of the wave equation in a nonplanar stratified medium [J. Math. Phys. 2 9, 36 (1988)] ⋮ Invariant imbedding and hyperbolic heat waves ⋮ Existence and construction of solutions of dissipative inverse problems ⋮ Three-dimensional electromagnetic inverse scattering for biisotropic dispersive media ⋮ Time domain Green functions technique for a point source over a dissipative stratified half-space with a phase velocity mismatch at the surface ⋮ An ill-posed problem of the continuation of transient data for a hyperbolic equation in a three-dimensional inhomogeneous half-space ⋮ Wave propagators for transient waves in one-dimensional media

Cites Work

• Obtaining scattering kernels using invariant imbedding
• Direct and inverse scattering in the time domain via invariant imbedding equations
• An electromagnetic inverse problem for dispersive media
• Direct and inverse scattering in the time domain for a dissipative wave equation. I. Scattering operators
• Direct and inverse scattering in the time domain for a dissipative wave equation. II. Simultaneous reconstruction of dissipation and phase velocity profiles
• Factorization of the wave equation in higher dimensions
• Factorization of the wave equation in a nonplanar stratified medium
• An inverse problem for an absorbing medium with multiple discontinuities

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