Advertisement

Differential Equations

, Volume 55, Issue 2, pp 205–219 | Cite as

Carleman Estimate for a Hyperbolic-Parabolic System

  • E. V. AmosovaEmail author
Partial Differential Equations
  • 12 Downloads

Abstract

A Carleman estimate is obtained for the solutions of a hyperbolic-parabolic system adjoint to the Navier–Stokes equations for a compressible medium.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fursikov, A.V. and Imanuvilov, O.Yu., On controllability of certain systems simulating a fluid flow, IMA J. Appl. Math., 1995, vol. 68, pp. 149–184.MathSciNetzbMATHGoogle Scholar
  2. 2.
    Fursikov, A.V. and Imanuvilov, O.Yu., On exact boundary zero-controllability of two-dimensional Navier–Stokes equations, Acta Appl. Math.. 1994, vol. 37, pp. 67–76.Google Scholar
  3. 3.
    Emanuilov, O.Yu., Exact controllability by semilinear parabolic equations, Vestn. Ross. Univ. Druzh. Nar. Ser. Mat., 1994, no. 1, pp. 109–116.zbMATHGoogle Scholar
  4. 4.
    Fursikov, A.V. and Imanuvilov, O.Yu., Controllability of Evolution Equations, in Lect. Notes Ser., Seoul Nat. Univ., 1996, Vol. 34.Google Scholar
  5. 5.
    Fabre, C., Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems, ESAIM Control Optim. Calc. Var., 1996, vol. 1, pp. 267–302.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Imanuvilov, O.Yu. and Yamamoto, M., On Carleman inequalities for parabolic equations in Sobolev spaces of negative order and exact controllability for semilinear parabolic equations, Publ. Res. Inst. Math. Sci., 2003, vol. 39, pp. 227–274.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Romanov, V.G., Carleman estimates for second-order hyperbolic equations, Sib. Math. J., 2006, vol. 47, no. 1, pp. 135–151.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Amosova, E.V., Analysis of the uniqueness and stability of hyperbolic-parabolic system, Dal’nevost. Mat. Zh., 2016. vol. 16, no. 2, pp. 123–136.Google Scholar
  9. 9.
    DiPerna, R.J. and Lions, P.L., Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 1989, vol. 98, pp. 511–547.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Fursikov, A.V., Optimal’noe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya (Optimal Control of Distributed Systems. Theory and Applications), Novosibirsk: Nauchn. Kniga, 1999.CrossRefzbMATHGoogle Scholar
  11. 11.
    Lions, J.-L. and Magenes, E., Problèmes aux limites nonhomogènes et applications, Paris: Dunod, 1968.zbMATHGoogle Scholar
  12. 12.
    Amosova, E.V., Carleman estimates of solutions of the Neumann problem for a parabolic equation, Dal’nevost. Mat. Zh., 2015, vol. 15, no. 1, pp. 3–20.MathSciNetzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Far Eastern Federal UniversityVladivostokRussia
  2. 2.Institute of Applied Mathematics of the Far Eastern Branch of the Russian Academy of SciencesVladivostokRussia

Personalised recommendations