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Communications in Mathematical Physics

, Volume 114, Issue 4, pp 527–536 | Cite as

Rarefactions and large time behavior for parabolic equations and monotone schemes

  • Eduard Harabetian
Article

Abstract

We consider the large time behavior of monotone semigroups associated with degenerate parabolic equations and monotone difference schemes. For an appropriate class of initial data the solution is shown to converge to rarefaction waves at a determined asymptotic rate.

Keywords

Neural Network Statistical Physic Complex System Initial Data Nonlinear Dynamics 
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.

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References

  1. 1.
    Osher, S., Ralston, J.:L 1 Stability of travelling waves with applications to convective porous media flow. Commun. Pure. Appl. Math.35, 737–751 (1982)Google Scholar
  2. 2.
    Volpert, A. I., Hudjaev, S. I.: Cauchy's problem for degenerate second order quasilinear parabolic equations. Math. USSR Sb.7, 365–387 (1969)Google Scholar
  3. 3.
    Jennings, G.: Discrete shocks. Commun. Pure. Appl. Math.27, 25–37 (1974)Google Scholar
  4. 4.
    Il'in, A. M., Oleinik, O. A.: Behavior of the solutions of the Cauchy problem for certain quasilinear equations for unbounded increase of the time. Am. Math. Soc. Transl. Series 2,42, 19–23 (1964)Google Scholar
  5. 5.
    Friedman, A.: Partial differential equations of parabolic type. New York: Prentice Hall 1964Google Scholar
  6. 6.
    Kuznetsov, N. N.: On Stable methods for solving non-linear first order partial differential equations in the class of discontinuous functions. Topics in numerical analysis, III (Proc. Roy. British Acad. Conf., Trinity Coll., Dublin 1976), pp. 183–197Google Scholar
  7. 7.
    Crandall, M., Majda, A.: Monotone difference approximations for scalar conservation laws. Math. Comp.34, 1–22 (1980)Google Scholar
  8. 8.
    Sanders, R.: On convergence of monotone finite difference schemes with variable spatial differencing. Math. Comp.40, 91–106 (1983)Google Scholar
  9. 9.
    Crandall, M., Tartar, L.: Some relations between nonexpansive and order preserving mappings. Proc. Am. Math. Soc.78, 385–390 (1980)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Eduard Harabetian
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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