Advertisement

Journal of Mathematical Sciences

, Volume 202, Issue 6, pp 859–868 | Cite as

On Blow-Up of Solutions of Some Systems of Quasilinear Parabolic Inequalities

  • A. Muravnik
Article
  • 26 Downloads

Abstract

We study systems of parabolic inequalities (including singular and degenerate ones), which contain squares of first derivatives of the unknown function with respect to spatial variables. We establish conditions that guarantee nonexistence of their global solutions.

Keywords

Global Solution Nontrivial Solution Order Singularity Nonlinear Parabolic Equation Quasilinear Parabolic Equation 
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.
    A. Bitsadze, Some Classes of Partial Differential Equations [in Russian], Nauka, Moscow (1981).Google Scholar
  2. 2.
    J.R. Burgan, A. Munier, M.R. Feix, and E. Fijalkow, “Homology and the nonlinear heat diffusion equation,” SIAM J. Appl. Math., 44, 11–18 (1984).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    G. Caristi, “Existence and nonexistence of global solutions of degenerate and singular parabolic systems,” Abstr. Appl. Anal., 5, No. 4, 265–284 (2000).MathSciNetCrossRefGoogle Scholar
  4. 4.
    V. Denisov and A. Muravnik, “On stablization of the solution to the Cauchy problem for quasilinear parabolic equations,” J. Differ. Equ., 38, No. 3, 369–374 (2002).MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    M. Kardar, G. Parisi, and Y.-C. Zhang, “Dynamic scaling of growing interfaces,” Phys. Rev. Lett., 56, 889–892 (1986).CrossRefMATHGoogle Scholar
  6. 6.
    E. Medina, T. Hwa, M. Kardar, and Y.-C. Zhang, “The Burgers equation with correlated noise: Renormalization group analysis and applications to directed polymers and interface growth,” Phys. Rev. A, 39, 3053–3075 (1989).MathSciNetCrossRefGoogle Scholar
  7. 7.
    E. Mitidieri and S. Pohozaev, “A priori estimates and nonexistence of solutions to nonlinear partial differential equations and inequalities,” Proc. Steklov Inst. Math., 234, 1–383 (2001).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.MoscowRussia

Personalised recommendations