Journal of East China Normal University(Natural Science) >

2022 , Vol. 2022 >Issue 1: 1 - 9

DOI: https://doi.org/10.3969/j.issn.1000-5641.2022.01.001

Mathematics

Stability of the solution to a singularly perturbed semilinear second-order differential equation with discontinuous right-hand side

  • Aleksei LIUBAVIN ,
  • Mingkang NI
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  • 1. School of Mathematical Sciences, East China Normal University, Shanghai　200241, China

Received date: 2021-01-18

  Online published: 2022-01-18

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Abstract

In this paper, a stationary problem for the reaction-diffusion equation with a discontinuous right-hand side is considered. Based on ideas from contrast structure theory, the asymptotic representations for eigenvalues and eigenfunctions are constructed by solving a Sturm-Liouville problem and an estimation of the remainder is obtained. Moreover, a sufficient condition which guarantees the stability of the solution to this task is established.

Key words： singular perturbations; asymptotic approximations; stability; reaction-diffusion equation

Cite this article

Aleksei LIUBAVIN , Mingkang NI . Stability of the solution to a singularly perturbed semilinear second-order differential equation with discontinuous right-hand side[J]. Journal of East China Normal University(Natural Science), 2022 , 2022(1) : 1 -9 . DOI: 10.3969/j.issn.1000-5641.2022.01.001

References

1 BUTUZOV V F, VASILEVA A B. Asymptotic of a solution of contrast-structure type [J]. Mathematical Notes of the Academy of Sciences of the USSR, 1987, 42: 956-961.
2 VASILEVA A B. On the stability of the contrast structures. Mathematical Modeling, 1991, (3/4): 114- 123.
3 VASILEVA A B. On the question of the stability of solutions to the type of contrast structures. Mathematical Modeling, 1990, (1/2): 119- 125.
4 NEFEDOV N N, NI M K. Internal layers in the one-dimensional reaction-diffusion equation with a discontinuous reactive term. Computational Mathematics & Mathematical Physics, 2015, 55 (12): 2001- 2007.
5 HENRY D. Geometric Theory of Semilinear Parabolic Equations [M]. Berlin: Springer-Verlag, 1981: 350.
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