Skip to main content
Log in

Increasing smoothness of solutions to some huperbolic problems

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. N. A. Ëltysheva, “To the question of stability of stationary solutions to some hyperbolic systems,” Dokl. Akad. Nauk SSSR,289, No. 1, 30–32 (1986).

    Google Scholar 

  2. N. A. Ëltysheva, “On qualitative properties of solutions to some hyperbolic systems on the plane,” Mat. Sb.,135, No. 2, 186–209 (1988).

    Google Scholar 

  3. T. I. Zelenyak, “On stationary solutions to the mixed problems arising in study of some chemical processes,” Differentsial'nye Uravneniya,2, No. 2, 205–213 (1966).

    Google Scholar 

  4. V. È. Abolinya and A. D. Myshkis, “A. mixed problem for an almost linear hyperbolic system on the plane,” Mat. Sb.,50, No. 4, 423–442 (1960).

    Google Scholar 

  5. V. È. Abolinya and A. D. Myshkis, “On a mixed problem for an almost linear hyperbolic system on the plane,” Uchen. Zap. Latv. Univ.,20, No. 3, 87–104 (1958).

    Google Scholar 

  6. S. K. Godunov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  7. J. Rauch and M. Reed, “Jump discontinuities of semilinear, strictly hyperbolic systems in two variables: creation and propagation,” Comm. Math. Phys.,81, No. 2, 203–227 (1981).

    Article  MATH  Google Scholar 

  8. J. Rauch and M. Reed, “Nolinear microlocal analysis of semilinear hyperbolic systems in one space dimension,” Duke Math. J.,49, No. 2, 397–475 (1982).

    Article  MATH  Google Scholar 

  9. M. Oberguggenberger, “Propagation of singularities for semilinear hyperbolic initial-boundary value problems in one space dimension,” J. Differential Equations,61, No. 1, 1–39 (1986).

    Article  MATH  Google Scholar 

  10. K. V. Brushlinskiî, “On the growth of a solution to a mixed problem in the case when the system of eigenfunction is incomplete,” Izv. Akad. Nauk SSSR Ser. Mat.,23, No. 6, 893–912 (1959).

    Google Scholar 

  11. V. S. Sheplev and V. D. Meshcheryakov, “Mathematical modeling of reactors with fluidized bed of a catalyst,” in: Mathematical Modeling of Chemical Reactors [in Russian], Nauka, Novosibirsk, 1984, pp. 44–65.

    Google Scholar 

Download references

Authors

Additional information

The research is financially supported by the “Russian Universities” program (Grant MM7.8/3H-303-92) and the Russian Foundation for Basic Research (Grant 96-01-01618).

Novosibirsk. Translated fromSibirskiï matematicheskiï Zhurnal, Vol. 38, No. 1, pp. 109–124, January–February, 1997.

Translated by G. V. Dyatlov

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lavrent'ev, M.M., Lyul'ko, N.A. Increasing smoothness of solutions to some huperbolic problems. Sib Math J 38, 92–105 (1997). https://doi.org/10.1007/BF02674905

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02674905

Keywords

Navigation