One-Dimensional Inverse Problems of Mathematical Physics

Лаврентьев, М. М.; Reznitskaya, K. G.; Г, Яхно В

doi:10.1090/trans2/130

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Cited by 41 publications

(34 citation statements)

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“…We now examine Hadamard's example of an ill-posed problem [1,2]. Consider Cauchy problem for the Laplace's equation for any Sobolev norm [3] because the beats all polynomials in n (from any finite order of derivatives).…”

Section: Introductionmentioning

confidence: 99%

The Cauchy problem and Hadamard's example

Yaremko

Mogileva

2013

Global Journal of Mathematical Analysis

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Section: Introductionmentioning

confidence: 99%

The Cauchy problem and Hadamard's example

Yaremko

Mogileva

2013

Global Journal of Mathematical Analysis

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“…First of all, we can refer to the articles by A. N. Tikhonov [1], M. M. Lavrent ev [2][3][4], V. K. Ivanov [5], and their followers. More detailed information can be found in the monograph by A. M. Denisov [6].…”

Section: Introduction Statement Of the Problemmentioning

confidence: 99%

An inverse problem for an equation of elliptic-hyperbolic type with a nonlocal boundary condition

Сабитов

Martem’yanova

2012

Sib Math J

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We examine a mixed type equation with the Lavrent ev-Bitsadze operator and an unknown right-hand side in a rectangle and study a nonlocal boundary value problem in which the values of the stream function on the lateral sides of the rectangle are equal. The solution is given as a sum of a biorthogonal series. The uniqueness criterion and stability of solutions with respect to the boundary data are established.

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“…The problems in similar statements were investigated theoretically and numerically in [6,7,[10][11][12]. The article of Cheverda and Voronina [8] where the theorem of uniqueness of the minimum point of the data misfit functional was proved should be pointed out.…”

Section: Introductionmentioning

confidence: 99%

The inverse problem of acoustics: determination of source wavelet and velocity

Avdeev¹,

Goruynov²

1996

Journal of Inverse and Ill-Posed Problems

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This paper describes a numerical method for the solution of the inverse problem of acoustics in the case of recording of the full wave field at the free surface. The solution is sought by means of minimization of the data misfit functional which is a mean square deviation of the given wave field from the wave field calculated for some "test" medium model. The main attention is given to the problem of simultaneous determination of the form of the sounding signal and the velocity structure of the vertically-inhomogeneous medium in the case of the point source and receivers located at the free surface.

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One-Dimensional Inverse Problems of Mathematical Physics

Cited by 41 publications

References 0 publications

The Cauchy problem and Hadamard's example

The Cauchy problem and Hadamard's example

An inverse problem for an equation of elliptic-hyperbolic type with a nonlocal boundary condition

The inverse problem of acoustics: determination of source wavelet and velocity

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