Skip to main content
Log in

The cauchy problem for pseudoparabolic systems

  • 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. S. L. Sobolev, “On a new problem of mathematical physics,” Izv. Akad. Nauk SSSR Ser. Mat.,18, No. 1, 3–50 (1954).

    Google Scholar 

  2. I. G. Petrovskiî, Selected Works. Systems of Partial Differential Equations. Algebraic Geometry [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  3. S. A. Gal'pern, “The Cauchy problem for general systems of linear partial differential equations (avtoreferat doktorskoî dissertatsii),” Uspekhi Mat. Nauk,18, No. 2, 239–249 (1963).

    MATH  Google Scholar 

  4. V. N. Maslennikova, “The rate of decay of a vortex in a viscous fluid,” Trudy Mat. Inst. Steklov.,103, 117–141 (1968).

    MATH  Google Scholar 

  5. O. A. Ladyzhenskaya, Mathematical Problems of the Dynamics of a Viscous Incompressible Fluid [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  6. V. A. Solonnikov, “Estimates of the solution of a certain initial-boundary value problem for a linear nonstationary system of Navier-Stokes equations,” Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI),59, 178–254, (1976).

    Google Scholar 

  7. S. V. Uspenskiî, G. V. Demidenko, and V. G. Perepëlkin, Embedding Theorems and Applications to Differential Equations [in Russian], Nauka, Novosibirsk (1984).

    Google Scholar 

  8. G. V. Demidenko,L p-Theory of Boundary Value Problems for Equations of Sobolev Type [in Russian] [Preprint, No. 16], Inst. Mat. (Novosibirsk), Novosibirsk (1991).

    Google Scholar 

  9. G. V. Demidenko, “L p-theory of boundary value problems for equations of Sobolev type,” Siberian J. Differential Equations,1, No. 1, 17–54 (1995).

    Google Scholar 

  10. G. V. Demidenko, “Necessary conditions for the well-posedness of the Cauchy problem for a linearized Navier-Stokes system,” Sibirsk. Mat. Zh.,29, No. 3, 186–189 (1988).

    Google Scholar 

  11. G. V. Demidenko and I. I. Matveeva, “Boundary value problems in a quarter-space for the systems of non-Cauchy-Kovalevskaya type,” in: Numerical Methods and Models in Applied Mathematics. Trudy Inst. Mat. (Novosibirsk). Vol. 26 [in Russian], Ross. Akad. Nauk Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1994, pp. 54–78.

    Google Scholar 

  12. S. V. Uspenskiî, “On representation of functions determined by a certain class of hypoelliptic operators,” Trudy Mat. Inst. Steklov.,117, 292–299 (1972).

    Google Scholar 

  13. P. I. Lizorkin, “Generalized Liouville differentiation and the multiplier method in the theory of embeddings of classes of differentiable functions,” Trudy Mat. Inst. Steklov.,105, 89–167 (1969).

    MATH  Google Scholar 

Download references

Authors

Additional information

The research was financially supported by the Russian Foundation for Basic Research (Grant 95-01-01176).

Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 38, No. 6, pp. 1251–1266, November–December, 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Demidenko, G.V. The cauchy problem for pseudoparabolic systems. Sib Math J 38, 1084–1098 (1997). https://doi.org/10.1007/BF02675936

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02675936

Keywords

Navigation