Application of asymptotic analysis methods for solving a coefficient inverse problem for a system of nonlinear singularly perturbed reaction-diffusion equations with cubic nonlinearity

Authors

DOI:

https://doi.org/10.26089/NumMet.v20r432

Keywords:

singularly perturbed problem, interior and boundary layers, reaction-diffusion equation, inverse problem with the location of moving front data

Abstract

The capabilities of asymptotic analysis methods for solving a coefficient inverse problem for a system of nonlinear singularly perturbed equations of reaction-diffusion type with cubic nonlinearity are shown. The problem considered for a system of partial differential equations is reduced to a system of algebraic equations that is much simpler for a numerical study and relates the data of the inverse problem (the information on the position of the reaction front in time) with the coefficient to be recovered. Numerical results confirm the efficiency of the proposed approach.

Author Biographies

D.V. Lukyanenko

A.A. Melnikova

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Published

2019-10-29

How to Cite

Лукьяненко Д.В., Мельникова А.А. Application of Asymptotic Analysis Methods for Solving a Coefficient Inverse Problem for a System of Nonlinear Singularly Perturbed Reaction-Diffusion Equations With Cubic Nonlinearity // Numerical methods and programming. 2019. 20. 363-377. doi 10.26089/NumMet.v20r432

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Section

Section 1. Numerical methods and applications

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