Abstract:
We consider the problem of constructing a fundamental solution to a second order hyperbolic linear equation with variable coefficients depending on the space variable x∈Rn. Under the assumption of high but finite smoothness of the coefficients, we write out the structure of a fundamental solution, establish smoothness of the coefficients of the expansion of its singular part, and characterize smoothness of the regular part.
Keywords:
fundamental solution, second order hyperbolic equation, smoothness of solutions.
Citation:
V. G. Romanov, “On smoothness of a fundamental solution to a second order hyperbolic equation”, Sibirsk. Mat. Zh., 50:4 (2009), 883–889; Siberian Math. J., 50:4 (2009), 700–705
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\by V.~G.~Romanov
\paper On smoothness of a~fundamental solution to a~second order hyperbolic equation
\jour Sibirsk. Mat. Zh.
\yr 2009
\vol 50
\issue 4
\pages 883--889
\mathnet{http://mi.mathnet.ru/smj2011}
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\transl
\jour Siberian Math. J.
\yr 2009
\vol 50
\issue 4
\pages 700--705
\crossref{https://doi.org/10.1007/s11202-009-0080-x}
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Linking options:
https://www.mathnet.ru/eng/smj2011
https://www.mathnet.ru/eng/smj/v50/i4/p883
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Kokurin M.Yu., “Completeness of the Asymmetric Products of Solutions of a Second-Order Elliptic Equation and the Uniqueness of the Solution of An Inverse Problem For the Wave Equation”, Differ. Equ., 57:2 (2021), 241–250
A. I. Kozlov, M. Yu. Kokurin, “On Lavrent'ev-type integral equations in coefficient inverse problems for wave equations”, Comput. Math. Math. Phys., 61:9 (2021), 1470–1484
Rakesh, Sacks P., “Uniqueness for a hyperbolic inverse problem with angular control on the coefficients”, J. Inverse Ill-Posed Probl., 19:1 (2011), 107–126
Beilina L., Klibanov M.V., “Synthesis of global convergence and adaptivity for a hyperbolic coefficient inverse problem in 3D”, J. Inverse Ill-Posed Probl., 18:1 (2010), 85–132
Klibanov M.V., Fiddy M.A., Beilina L., Pantong N., Schenk J., “Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem”, Inverse Problems, 26:4 (2010), 045003, 30 pp.
Beilina L., Klibanov M.V., “Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm”, Inverse Problems, 26:12 (2010), 125009, 30 pp.
Beilina L., Klibanov M.V., “Global convergence for Inverse Problems”, Numerical Analysis and Applied Mathematics, AIP Conference Proceedings, 1281, 2010, 1056–1058
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