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

Lukyanenko, D.; Yeleskina, T.; Prigorniy, I.; Isaev, T.; Borzunov, A.; Shishlenin, M.

Статья опубликована в высокорейтинговом журнале

Информация о цитировании статьи получена из Web of Science, Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 9 апреля 2021 г.

Авторы: Lukyanenko D., Yeleskina T., Prigorniy I., Isaev T., Borzunov A., Shishlenin M.
Журнал: Mathematics
Том: 9
Номер: 4
Год издания: 2021
Издательство: MDPI
Местоположение издательства: Basel, Switzerland
Номер статьи: 342
DOI: 10.3390/math9040342
Аннотация: 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.
Добавил в систему: Лукьяненко Дмитрий Витальевич

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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 delayстатья

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