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, Maxim Shishlenin

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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 experi-mentally 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.

Original languageEnglish
Article number342
Pages (from-to)1-12
Number of pages12
JournalMathematics
Volume9
Issue number4
DOIs
Publication statusPublished - 2 Feb 2021

Keywords

  • Advection equa-tion; inverse problem with data on the reaction front position
  • Diffusion
  • Inverse problem of recovering the initial condition; reaction

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