Advertisement

Mathematical Notes

, Volume 104, Issue 5–6, pp 735–744 | Cite as

Contrast Structures in Problems for a Stationary Equation of Reaction-Diffusion-Advection Type with Discontinuous Nonlinearity

  • Yafei Pan
  • Mingkang NiEmail author
  • M. A. Davydova
Article
  • 10 Downloads

Abstract

A singularly perturbed boundary-value problem for a nonlinear stationary equation of reaction-diffusion-advection type is studied. A new class of problems with discontinuous advective and reactive terms is considered. The existence of contrast structures in problems of this type is proved, and an asymptotic approximation of the solution with an internal transition layer of arbitrary order of accuracy is obtained.

Keywords

problem of reaction-diffusion-advection type internal transition layer asymptotic methods problems with discontinuous nonlinearity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    N. N. Nefedov and M. K. Ni, “Internal layers in the one-dimensional reaction-diffusion equation with a discontinuous reactive term,” Zh. Vychisl.Mat. Mat. Fiz. 55 (12), 2042–2048 (2015) [Comput. Math. Math. Phys. 55 (12), 2001–2007 (2015)].MathSciNetzbMATHGoogle Scholar
  2. 2.
    N. T. Levashova, N. N. Nefedov, and A. O. Orlov, “Time-independent reaction-diffusion equation with a discontinuous reactive term,” Zh. Vychisl. Mat. Mat. Fiz. 57 (5), 854–866 (2017) [Comput. Math. Math. Phys. 57 (5), 854–866 (2017)].MathSciNetzbMATHGoogle Scholar
  3. 3.
    A. B. Vasil’eva, V. F. Butuzov, and N. N. Nefedov, “Singularly perturbed problems with boundary and internal layers,” in Trudy Mat. Inst. Steklova, Vol. 268: Differential Equations and Topology. I (MAIK “Nauka/Interperiodika,” Moscow, 2010), pp. 268–283 [Proc. Steklov Inst.Math. 268, 258–273 (2010)].Google Scholar
  4. 4.
    N. N. Nefedov and M. A. Davydova, “Contrast structures in multidimensional singularly perturbed reaction-diffusion-advection problems,” Differ. Uravn. 48 (5), 738–748 (2012) [Differ. Equations 48 (5), 745–755 (2012)].MathSciNetzbMATHGoogle Scholar
  5. 5.
    N. N. Nefedov, L. Recke, and K. R. Schneider, “Existence and asymptotic stability of periodic solutions with an internal layer of reaction-advection-diffusion equations,” J. Math. Anal. Appl. 405 (1), 90–103 (2013).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    M. A. Davydova and N. N. Nefedov, “Existence and stability of contrast structures in multidimensional singularly perturbed reaction-diffusion-advection problems,” in Lecture Notes in Comput. Sci., Vol. 10187: Numerical Analysis and Its Applications (Springer, Cham, 2017), pp. 277–285.Google Scholar
  7. 7.
    A. B. Vasil’eva and V. F. Butuzov, Asymptotic Methods in the Theory of Singular Perturbations in Current Problems in Applied and Computational Mathematics (Vyssh. Shkola, Moscow, 1990) [in Russian].Google Scholar
  8. 8.
    M. A. Davydova, “Existence and stability of solutions with boundary layers in multidimensional singularly perturbed reaction-diffusion-advection problems,” Mat. Zametki 98 (6), 853–864 (2015) [Math. Notes 98 (6), 909–919 (2015)].MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.East China Normal UniversityShanghaiPeople’s Republic of China
  2. 2.LomonosovMoscow State UniversityMoscowRussia

Personalised recommendations