Inverse Problem of Recovering the Initial Condition for a Nonlinear Equation of the Reaction–Diffusion–Advection Type by Data Given on the Position of a Reaction Front with a Time Delay

Dmitry Lukyanenko, Tatyana Yeleskina, Igor Prigorniy, Temur Isaev, Andrey Borzunov and Maxim Shishlenin
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Dmitry Lukyanenko: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Tatyana Yeleskina: Faculty of Physics, Lomonosov Moscow State University, Baku Branch, Baku 1143, Azerbaijan
Igor Prigorniy: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Temur Isaev: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Andrey Borzunov: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Maxim Shishlenin: Institute of Computational Mathematics and Mathematical Geophysics of SB RAS, 630090 Novosibirsk, Russia

Mathematics, 2021, vol. 9, issue 4, 1-12

Abstract: In this paper, approaches to the numerical recovering of the initial condition in the inverse problem for a nonlinear singularly perturbed reaction–diffusion–advection equation are considered. The feature of the formulation of the inverse problem is the use of additional information about the value of the solution of the equation at the known position of a reaction front, measured experimentally with a delay relative to the initial moment of time. In this case, for the numerical solution of the inverse problem, the gradient method of minimizing the cost functional is applied. In the case when only the position of the reaction front is known, the method of deep machine learning is applied. Numerical experiments demonstrated the possibility of solving such kinds of considered inverse problems.

Keywords: inverse problem of recovering the initial condition; reaction–diffusion–advection equation; inverse problem with data on the reaction front position (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 (2)

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