Multidimensional inverse problem for the acoustic equation in the ray statement

被引：0

作者：

Yakhno, VG ^{[1
]}

机构：

[1] Russian Acad Sci, Sobolev Inst Math, Novosibirsk 630090, Russia

来源：

INVERSE PROBLEMS IN UNDERWATER ACOUSTICS | 2001年

关键词：

D O I：

暂无

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

This chapter deals with a multidimensional inverse dynamic problem for the acoustic equation. This problem is reduced to inverse kinematic, integral geometry problems, a Dirichlet problem for a quasilinear elliptic equation, and for some special case to standard tomography problems. The structure and some properties of the fundamental solution of the Cauchy problem for the acoustic equation are used for this reduction. The structure and properties are described in detail.

引用

页码：159 / 183

页数：25

共 50 条

[41] Ray Statement of the Acoustic Tomography Problem (vol 106, pg 254, 2022)
Romanov, V. G.
DOKLADY MATHEMATICS, 2022, 106 (03) : 488 - 488
[42] On the Uniqueness of the Solution of the Inverse Coefficient Problem for the Helmholtz Equation in a Phaseless Spatially Nonoverdetermined Statement
Kokurin, M. Yu.
DIFFERENTIAL EQUATIONS, 2021, 57 (09) : 1136 - 1141
[43] On the Uniqueness of the Solution of the Inverse Coefficient Problem for the Helmholtz Equation in a Phaseless Spatially Nonoverdetermined Statement
M. Yu. Kokurin
Differential Equations, 2021, 57 : 1136 - 1141
[44] STATEMENT AND SOLUTION OF AN INVERSE CONTACT PROBLEM
MITKEVICH, VM
DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1984, (05): : 38 - 40
[45] Variational statement of an inverse problem for a domain
Niftiyev, A. A.
Akhmedov, E. R.
DIFFERENTIAL EQUATIONS, 2007, 43 (10) : 1445 - 1452
[46] Variational statement of an inverse problem for a domain
A. A. Niftiyev
E. R. Akhmedov
Differential Equations, 2007, 43 : 1445 - 1452
[47] Inverse backscattering for the acoustic equation
Stefanov, P
Uhlmann, G
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1997, 28 (05) : 1191 - 1204
[48] Inverse problem of determining the absorption coefficient in the multidimensional heat equation with unlimited minor coefficients
Bukharova, T. I.
Kamynin, V. L.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2015, 55 (07) : 1164 - 1176
[49] The variational formulation of an inverse problem for multidimensional nonlinear time-dependent Schrodinger equation
Aksoy, Nigar Yildirim
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2016, 24 (05): : 559 - 571
[50] An Representation of the Solution of the Inverse Problem for a Multidimensional Parabolic Equation with Initial Data in the Form of a Product
Frolenkov, I., V
Romanenko, G., V
JOURNAL OF SIBERIAN FEDERAL UNIVERSITY-MATHEMATICS & PHYSICS, 2012, 5 (01): : 122 - 131

← 1 2 3 4 5 →