Advertisement

Comparison Principle for Reaction-Diffusion-Advection Problems with Boundary and Internal Layers

  • Nikolay Nefedov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)

Abstract

In the present paper we discuss father development of the general scheme of the asymptotic method of differential inequalities and illustrate it applying for some new important cases of initial boundary value problem for the nonlinear singularly perturbed parabolic equations,which are called in applications as reaction-diffusion-advection equations. The theorems which state front motion description and stationary contrast structures formation are proved for parabolic, parabolic-periodic and integro-parabolic problems.

Keywords

singularly perturbed problems comparison principle reaction-diffusion-advection equations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Vasilieva, A.B., Butuzov, V.F., Nefedov, N.N.: Contrast structures in singularly perturbed problems. Fundamentalnaja i Prikladnala Matemat. 3(4), 799–851 (1998) (in Russian)Google Scholar
  2. 2.
    Amann, H.: Periodic Solutions of Semilinear Parabolic Equations. In: Nonlinear Analysis: a Collection of Papers in Honor of Erich Rothe, pp. 1–29. Academic, New York (1978)Google Scholar
  3. 3.
    Sattinger, D.H.: Monotone Methods in Elliptic and Parabolic Boundary Value Problems. Indiana Univ. Math. J. 21(11), 979–1001 (1972)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Hess, P.: Periodic-Parabolic Boundary Value Problems and Positivity. Pitman Research Notes in Math. Series, vol. 247. Longman Scientific&Technical, Harlow (1991)zbMATHGoogle Scholar
  5. 5.
    Amann, H.: Maximum priciples and principal eigenvalues. In: Ten Mahtmatical Essays in Analysis and Topology. Elsevier (2005)Google Scholar
  6. 6.
    Zabrejko, P.P., Koshelev, A.I., Krasnoseiskij, M.A et al.: Integral equations. M.: Nauka (1968) (in Russian)Google Scholar
  7. 7.
    Nefedov, N.N.: The Method of Differential Inequalities for Some Classes of Nonlinear Singularly Perturbed Problems with Internal Layers. Differ. Uravn. 31(7), 1142–1149 (1995)MathSciNetGoogle Scholar
  8. 8.
    Vasileva, A.B., Butuzov, V.F., Nefedov, N.N.: Singularly Perturbed problems with Boundary and Internal Layers. Proceedings of the Steklov Institute of Mathmatics 268, 258–273 (2010)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Nefedov, N.N., Nikitin, A.G., Petrova, M.A., Recke, L.: Moving fronts in integro-parabolic reaction-diffusion-advection equations. Differ. Uravn. 47(9), 1–15 (2011)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Nikolay Nefedov
    • 1
  1. 1.Department of Mathematics, Faculty of PhysicsLomonosov Moscow State UniversityMoscowRussia

Personalised recommendations