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

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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 delay. / Lukyanenko, Dmitry; Yeleskina, Tatyana; Prigorniy, Igor et al.

In: Mathematics, Vol. 9, No. 4, 342, 02.02.2021, p. 1-12.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{0efd413d739745a893ab8c4fd4914159,

title = "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",

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.",

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

author = "Dmitry Lukyanenko and Tatyana Yeleskina and Igor Prigorniy and Temur Isaev and Andrey Borzunov and Maxim Shishlenin",

note = "Funding Information: Funding: The reported study was funded by RFBR, project number 20-31-70016. Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

year = "2021",

month = feb,

day = "2",

doi = "10.3390/math9040342",

language = "English",

volume = "9",

pages = "1--12",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI AG",

number = "4",

}

RIS

TY - JOUR

T1 - 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

AU - Lukyanenko, Dmitry

AU - Yeleskina, Tatyana

AU - Prigorniy, Igor

AU - Isaev, Temur

AU - Borzunov, Andrey

AU - Shishlenin, Maxim

N1 - Funding Information: Funding: The reported study was funded by RFBR, project number 20-31-70016. Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/2/2

Y1 - 2021/2/2

N2 - 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.

AB - 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.

KW - Advection equa-tion; inverse problem with data on the reaction front position

KW - Diffusion

KW - Inverse problem of recovering the initial condition; reaction

UR - http://www.scopus.com/inward/record.url?scp=85101020827&partnerID=8YFLogxK

U2 - 10.3390/math9040342

DO - 10.3390/math9040342

M3 - Article

AN - SCOPUS:85101020827

VL - 9

SP - 1

EP - 12

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 4

M1 - 342

ER -

ID: 27965169