Existence and stability of a stationary solution of the system of diffusion equations in a medium with discontinuous characteristics under ... View Full Text


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Article Info

DATE

2022-07-26

AUTHORS

N. T. Levashova, B. V. Tishchenko

ABSTRACT

Asymptotic analysis is used to study the existence, local uniqueness, and asymptotic stability in the sense of Lyapunov of a solution of a one-dimensional nonlinear system of reaction–diffusion equations with various types of quasimonotonicity of the functions describing reactions. A feature of the problem is the discontinuities (jumps) of these functions at a single point on the segment on which the problem is posed. The solution with a large gradient in the vicinity of the discontinuity point is studied. Sufficient conditions for the existence of a stable stationary solution of systems with various quasimonotonicity conditions are given. The asymptotic method of differential inequalities is used to prove the existence and stability theorems. The main distinctive features of this method for various types of quasimonotonicity are listed. More... »

PAGES

944-961

References to SciGraph publications

  • 2002-04. Method of Upper and Lower Solutions for Parabolic-Type Equations with Discontinuous Nonlinearities in DIFFERENTIAL EQUATIONS
  • 2021-12. Development of Methods of Asymptotic Analysis of Transition Layers in Reaction–Diffusion–Advection Equations: Theory and Applications in COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
  • 2021-11. Existence and Stability of the Solution to a System of Two Nonlinear Diffusion Equations in a Medium with Discontinuous Characteristics in COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
  • 1977-12. The approach of solutions of nonlinear diffusion equations to travelling front solutions in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2015-11. Existence and stability of solutions with boundary layers in multidimensional singularly perturbed reaction-diffusion-advection problems in MATHEMATICAL NOTES
  • 2020-09. On a Periodic Inner Layer in the Reaction–Diffusion Problem with a Modular Cubic Source in COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
  • 2012-11-17. Steplike contrast structure in a singularly perturbed system of equations with different powers of small parameter in COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
  • 2021-09. The Existence, Local Uniqueness, and Asymptotic Stability of the Boundary Layer Type Solution of the Neumann Problem for a Two-Equation Nonlinear System with Different Powers of a Small Parameter in MOSCOW UNIVERSITY PHYSICS BULLETIN
  • 2016-01-08. Extremal solutions for nonvariational quasilinear elliptic systems via expanding trapping regions in MONATSHEFTE FÜR MATHEMATIK
  • 2012-05. Contrast structures in multidimensional singularly perturbed reaction-diffusion-advection problems in DIFFERENTIAL EQUATIONS
  • 2015-12-08. Internal layers in the one-dimensional reaction–diffusion equation with a discontinuous reactive term in COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
  • 2017-04-12. Front Dynamics in an Activator-Inhibitor System of Equations in NUMERICAL ANALYSIS AND ITS APPLICATIONS
  • 2022-03-23. Contrast Structures in the Reaction-Diffusion-Advection Problem in the Case of a Weak Reaction Discontinuity in RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS
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    DOI

    http://dx.doi.org/10.1134/s0040577922070054

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