Inverse Problem for an Equation of the Reaction-Diffusion-Advection Type with Data on the Position of a Reaction Front: Features of the Solution in the Case of a Nonlinear Integral Equation in a Reduced Statement

Raul Argun, Alexandr Gorbachev, Natalia Levashova and Dmitry Lukyanenko
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Raul Argun: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Alexandr Gorbachev: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Natalia Levashova: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Dmitry Lukyanenko: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia

Mathematics, 2021, vol. 9, issue 18, 1-14

Abstract: The paper considers the features of numerical reconstruction of the advection coefficient when solving the coefficient inverse problem for a nonlinear singularly perturbed equation of the reaction-diffusion-advection type. Information on the position of a reaction front is used as data of the inverse problem. An important question arises: is it possible to obtain a mathematical connection between the unknown coefficient and the data of the inverse problem? The methods of asymptotic analysis of the direct problem help to solve this question. But the reduced statement of the inverse problem obtained by the methods of asymptotic analysis contains a nonlinear integral equation for the unknown coefficient. The features of its solution are discussed. Numerical experiments demonstrate the possibility of solving problems of such class using the proposed methods.

Keywords: coefficient inverse problem; reaction-diffusion-advection equation; singularly perturbed problem; inverse problem with data on the position of a reaction front (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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