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On an Exactly Solvable Nonlinear Diffusion Equation

  • Junkichi Satsuma
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 30)

Abstract

A nonlinear integro-differential equation describing a diffusion process with non-local mutual interaction is considered. It can be exactly linearized by a dependent variable transformation. A perturbational approach is employed to understand the structure of solutions of the equation. First, a series of differential equations approximating the integro-differential equation is derived. Then the effect of higher order corrections on the equilibrium solution is investigated.

Keywords

Exact Solution Equilibrium Solution High Order Correction Variable Transformation Perturbational Approach 
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References

  1. 1.
    J.M.Burgers: Adv. Appl. Mech. 1, 171 (1948)CrossRefGoogle Scholar
  2. 2.
    J.Satsuma: J. Phys. Soc. Jpn. 50, 1423 (1981)CrossRefGoogle Scholar
  3. 3.
    T.Kawahara and M.Tanaka: Phys. Lett. 97A, 311 (1983)CrossRefGoogle Scholar
  4. 4.
    K.Nozaki and N.Bekki: J. Phys. Soc. Jpn. 53, 1581 (1984)CrossRefGoogle Scholar
  5. 5.
    J.Satsuma and M.Mimura: preprint, “Exact Treatment of Nonlinear Diffusion Equations with Singular Integral Terms”Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Junkichi Satsuma
    • 1
  1. 1.General EducationMiyazaki Medical CollegeKiyotake, MiyazakiJapan

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