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007			cr cnu||||||||
008			240724s2002 xx o ||||0 eng d
020			_a9783110943849 _q(electronic bk.)
020			_z9789067643610
035			_a(MiAaPQ)EBC3049581
035			_a(Au-PeEL)EBL3049581
035			_a(CaPaEBR)ebr11008961
035			_a(CaONFJC)MIL807324
035			_a(OCoLC)922950405
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQC20.7.D5 -- R64 2002eb
100	1		_aRomanov, Vladimir G.
245	1	0	_aInvestigation Methods for Inverse Problems.
250			_a1st ed.
264		1	_aBerlin/Boston : _bDe Gruyter, Inc., _c2002.
264		4	_c©2002.
300			_a1 online resource (292 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aInverse and Ill-Posed Problems Series ; _vv.34
505	0		_aIntro -- Preface -- 1 Introduction -- 1.1 One-dimensional inverse kinematics problem -- 1.2 Inverse dynamical problem for a string -- 1.3 Inverse problems for a layered medium -- 2 Ray statements of inverse problems -- 2.1 Posing of the inverse problems -- 2.2 Asymptotic expansion -- 2.2.1 Asymptotic expansion of the solution -- 2.2.2 Reduction of the inverse problem -- 2.2.3 Construction of τ(x, y) -- 2.2.4 Proof of the expansion in the odd-dimensional case -- 2.2.5 Proof of the expansion in the even-dimensional case -- 2.2.6 Proof of the auxiliary lemma -- 2.3 Uniqueness theorems for the inverse problem -- 2.3.1 A proof of the stability estimate for the integral geometry problem -- 2.3.2 Uniqueness theorem for the integral geometry problem related to a vector field -- 2.3.3 Proof of the uniqueness theorem for inverse kinematics problem -- 2.3.4 The wave equation with an attenuation -- 2.3.5 Concluding remarks -- 2.4 Inverse problems related to a local heterogeneity -- 3 Local solvability of some inverse problems -- 3.1 Banach's spaces of analytic functions -- 3.2 Determining coefficients of the lower terms -- 3.2.1 Determining a coefficient of the lower term -- 3.2.2 Determining an attenuation coefficient -- 3.3 Determining the speed of the sound -- 3.4 A regularization method for solving an inverse problem -- 3.4.1 Theorems related to the system of integro-differential equations -- 3.4.2 Estimates of a solution to the algebraic equations -- 3.4.3 Convergence the approximate solution to the exact one -- 4 Inverse problems with single measurements -- 4.1 Determining coefficient of the lowest term -- 4.1.1 Statement of the problem and stability estimates -- 4.1.2 Proof of the stability theorems -- 4.1.3 Proof of Lemma 4.1.3 -- 4.1.4 Proof of Lemma 4.1.4 -- 4.2 Determining coefficients under first derivatives.
505	8		_a4.3 Determining the speed of sound in the wave equation -- 4.3.1 Formulation of the problem and a stability estimate of the solution -- 4.3.2 Proof of Theorem 4.3.1 -- 4.3.3 Proof of Lemma 4.3.5 -- 4.3.4 Proof of Lemma 4.3.6 -- 4.3.5 Proof of the inequality (4.3.24) -- 4.4 Case of a point source -- 4.4.1 Formulations of the problem and results -- 4.4.2 Proofs of the stability theorems -- 4.4.3 Properties of a solution to problem (4.4.1) -- 4.4.4 Proof of Lemma 4.4.3 -- 4.4.5 Proof of Lemma 4.4.4 -- 5 Stability estimates related to inverse problems for the transport equation -- 5.1 The problem of determining the relaxation and a density of inner sources -- 5.1.1 Statement of basic and auxiliary problems -- 5.1.2 The basic results -- 5.1.3 Proof of Theorem 5.1.1 -- 5.1.4 Proof of the auxiliary lemmas -- 5.2 A stability estimate in the problem of determining the dispersion index and relaxation in 2D -- 5.2.1 Statement of the problem and the basic results -- 5.2.2 Proof of Lemma 5.2.1 -- 5.2.3 A priori estimates -- 5.2.4 Proof of Theorem 5.2.3 -- 5.3 The problem of determining the dispersion index and relaxation in 3D -- 5.3.1 Statement of the problem and the main results -- 5.3.2 Proof of Lemma 5.3.1 -- 5.3.3 A priori estimates for function ω(x, v) -- 5.3.4 Estimates for functions ώ(x, v) and σ̃(x) -- 5.3.5 A priori estimates and differential properties of function u¯(x,v,v°) -- 5.3.6 A priori estimates and properties of function v(x, v,v°) -- 5.3.7 Equations for the derivatives of function ṽ(x, u, v°) -- 5.3.8 Proof of inequality (5.3.24) -- 5.3.9 Proof of inequality (5.3.25) -- 5.3.10 Proof of inequality (5.3.26) -- 5.3.11 Auxiliary formulae -- Bibliography.
520			_aThe Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aInverse problems (Differential equations) -- Numerical solutions.
650		0	_aMathematical physics.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aRomanov, Vladimir G. _tInvestigation Methods for Inverse Problems _dBerlin/Boston : De Gruyter, Inc.,c2002 _z9789067643610
797	2		_aProQuest (Firm)
830		0	_aInverse and Ill-Posed Problems Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3049581 _zClick to View
999			_c65232 _d65232