Differential Equations

, Volume 47, Issue 9, pp 1318–1332 | Cite as

Moving fronts in integro-parabolic reaction-advection-diffusion equations

  • N. N. Nefedov
  • A. G. Nikitin
  • M. A. Petrova
  • L. Recke
Integral Equations

Abstract

We consider initial-boundary value problems for a class of singularly perturbed nonlinear integro-differential equations. In applications, they are referred to as nonlocal reactionadvection-diffusion equations, and their solutions have moving interior transition layers (fronts). We construct the asymptotics of such solutions with respect to a small parameter and estimate the accuracy of the asymptotics. To justify the asymptotics, we use the asymptotic differential inequality method.

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • N. N. Nefedov
    • 1
    • 2
    • 3
  • A. G. Nikitin
    • 1
    • 2
    • 3
  • M. A. Petrova
    • 1
    • 2
    • 3
  • L. Recke
    • 1
    • 2
    • 3
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.National Research Nuclear University MEPhIMoscowRussia
  3. 3.Humboldt-Universität zu BerlinBerlinGermany

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