Advertisement

Ukrainian Mathematical Journal

, Volume 55, Issue 8, pp 1383–1393 | Cite as

On the Asymptotic Behavior of Solutions of the First Initial Boundary-Value Problems for Parabolic Equations

  • Nguyen Manh Hung
  • Tran Thi Loan
Article
  • 20 Downloads

Abstract

We consider the first initial boundary-value problem for a strongly parabolic system on an infinite cylinder with nonsmooth boundary. We prove some results on the existence, uniqueness, and asymptotic behavior of solutions as t → ∞.

Keywords

Asymptotic Behavior Parabolic Equation Parabolic System Infinite Cylinder Nonsmooth Boundary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    V. A. Kondrat'ev and O. A. Oleinik, “Boundary-value problems for a partial differential equation in nonsmooth domains,” Usp. Mat. Nauk, 38, Issue 2, 3-76 (1983).Google Scholar
  2. 2.
    S. A. Nazarov and B. A. Plamenevskii, Elliptic Problems in Domains with Piecewise-Smooth Boundary [in Russian], Nauka, Moscow (1991).Google Scholar
  3. 3.
    O. A. Ladyzhenskaya, Boundary-Value Problems in Mathematical Physics [in Russian], Nauka, Moscow (1973).Google Scholar
  4. 4.
    Nguyen Manh Hung, “On smoothness of solutions of Dirichlet problems for hyperbolic systems in domains with conical or angular points,” Dokl. Akad. Nauk SSSR, 362, No. 2, 161-164 (1998).Google Scholar
  5. 5.
    O. A. Ladyzhenskaya, “On nonstationary operator equations and their applications to linear problems of mathematical physics,” Mat. Sb., 45, No. 2, 123-158 (1958).Google Scholar
  6. 6.
    Doan Vanh Nhok, “Asymptotics of solutions of boundary-value problems for parabolic equations of the second order in the neighborhood of an angular point of the boundary,” Vestn. Mosk. Univ., Ser. Mat. Mekh., No. 1, 34-36 (1984).Google Scholar
  7. 7.
    Chan Zui Kho and G. I. Éskin, “Boundary-value problems for parabolic systems of pseudodifferential equations,” Dokl. Akad. Nauk SSSR, 198, No. 1, 50-53 (1971).Google Scholar
  8. 8.
    V. N. Aref'ev and V. A. Kondrat'ev, “Asymptotic behavior of solutions of the second boundary-value problem for nonlinear parabolic equations,” Differents. Uravn., 29, No. 12, 2104-2116 (1993).Google Scholar
  9. 9.
    G. Fichera, Existence Theorems in Elasticity Theory [Russian translation], Mir, Moscow (1974).Google Scholar
  10. 10.
    J. Nash, “Continuity of solutions of parabolic and elliptic equations,” Amer. J. Math., 80, 931-984 (1958).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Nguyen Manh Hung
    • 1
  • Tran Thi Loan
    • 1
  1. 1.Hanoi Pedagogic InstituteHanoiVietnam

Personalised recommendations