Skip to main content
SpringerLink
Log in

Mathematical Problems of Tomography and Hyperbolic Mappings

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We consider a new class of mathematical problems related to interpretation of tomography data. The main assumption is that the sought distribution of absorption is an identically one function in the domain to be determined. These problems are connected with three known directions of mathematical physics: the Dirichlet problems for hyperbolic equations, the problems of small oscillations of a rotating fluid, and the problems of supersonic flows of an ideal gas.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Pikalov V. V. and Preobrazhenskiî N. G., Reconstructive Tomography in Gas Dynamics and Plasma Physics [in Russian], Nauka, Novosibirsk (1987).

    Google Scholar 

  2. Natterer F., The Mathematics of Computerized Tomography [Russian translation], Mir, Moscow (1990).

    Google Scholar 

  3. Nikolaev A. V., “Seismology: scientific and technological revolution and problems of XXI century,” in: Mathematical Modeling in Geophysics [in Russian], Nauka, Novosibirsk, 1968.

    Google Scholar 

  4. John F., “The Dirichlet problem for a hyperbolic equation,” Amer. J. Math., 63, No. 1, 141-154 (1941).

    Google Scholar 

  5. Aleksandryan R. A., “On one Sobolev problem for special fourth-order partial differential equations,” Dokl. Akad. Nauk SSSR, 73, No. 4, 631-634 (1950).

    Google Scholar 

  6. Zelenyak T. I., Selected Questions of Qualitative Theory of Partial Differential Equations [in Russian], Novosibirsk Univ., Novosibirsk (1970).

    Google Scholar 

  7. Lavrent'ev M. M., “On a certain boundary value problem for a hyperbolic system,” Mat. Sb., 38, No. 4, 451-464 (1956).

    Google Scholar 

  8. Shabat B. V., “On an analog of the Riemann theorem for linear hyperbolic systems of differential equations,” Uspekhi Mat. Nauk, 11, No. 5, 101-105 (1956).

    Google Scholar 

  9. Shabat B. V., “On certain hyperbolic quasiconformal mappings,” in: Some Problems of Mathematics and Mechanics [in Russian], Nauka, Leningrad, 1970.

    Google Scholar 

  10. Lavrent'ev M. A. and Shabat B. V., Problems of Hydrodynamics and Their Mathematical Models [in Russian], Nauka, Moscow (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Sobolev Institute of Mathematics, Novosibirsk

    M. M. Lavrent'ev

Authors
  1. M. M. Lavrent'ev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lavrent'ev, M.M. Mathematical Problems of Tomography and Hyperbolic Mappings. Siberian Mathematical Journal 42, 916–925 (2001). https://doi.org/10.1023/A:1011915727315

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011915727315

Keywords

Search

Navigation