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Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front. / Lukyanenko, D. V.; Borzunov, A. A.; Shishlenin, M. A.

в: Communications in Nonlinear Science and Numerical Simulation, Том 99, 105824, 08.2021.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Lukyanenko, DV, Borzunov, AA & Shishlenin, MA 2021, 'Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front', Communications in Nonlinear Science and Numerical Simulation, Том. 99, 105824. https://doi.org/10.1016/j.cnsns.2021.105824

APA

Lukyanenko, D. V., Borzunov, A. A., & Shishlenin, M. A. (2021). Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front. Communications in Nonlinear Science and Numerical Simulation, 99, [105824]. https://doi.org/10.1016/j.cnsns.2021.105824

Vancouver

Lukyanenko DV, Borzunov AA, Shishlenin MA. Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front. Communications in Nonlinear Science and Numerical Simulation. 2021 авг.;99:105824. doi: 10.1016/j.cnsns.2021.105824

Author

Lukyanenko, D. V. ; Borzunov, A. A. ; Shishlenin, M. A. / Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front. в: Communications in Nonlinear Science and Numerical Simulation. 2021 ; Том 99.

BibTeX

@article{c906ea5e98d54b55a826d316efe8c446,
title = "Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front",
abstract = "An approach to solving coefficient inverse problems for nonlinear reaction-diffusion-advection equations is proposed. As an example, we consider an inverse problem of restoring a coefficient in a nonlinear Burgers-type equation. One of the features of the inverse problem is a use of additional information about the position of a reaction front. Another feature of the approach is a use of asymptotic analysis methods to select a good initial guess in a gradient method for minimizing a cost functional that occurs when solving the coefficient inverse problem. Numerical experiments demonstrate the effectiveness of the proposed approach.",
keywords = "Coefficient inverse problem, Inverse problem with data on the position of a reaction front, Reaction-diffusion-advection equation, Singularly perturbed problem",
author = "Lukyanenko, {D. V.} and Borzunov, {A. A.} and Shishlenin, {M. A.}",
note = "Funding Information: The reported study was funded by RFBR, project number 20-31-70016. Publisher Copyright: {\textcopyright} 2021 Elsevier B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = aug,
doi = "10.1016/j.cnsns.2021.105824",
language = "English",
volume = "99",
journal = "Communications in Nonlinear Science and Numerical Simulation",
issn = "1007-5704",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front

AU - Lukyanenko, D. V.

AU - Borzunov, A. A.

AU - Shishlenin, M. A.

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

PY - 2021/8

Y1 - 2021/8

N2 - An approach to solving coefficient inverse problems for nonlinear reaction-diffusion-advection equations is proposed. As an example, we consider an inverse problem of restoring a coefficient in a nonlinear Burgers-type equation. One of the features of the inverse problem is a use of additional information about the position of a reaction front. Another feature of the approach is a use of asymptotic analysis methods to select a good initial guess in a gradient method for minimizing a cost functional that occurs when solving the coefficient inverse problem. Numerical experiments demonstrate the effectiveness of the proposed approach.

AB - An approach to solving coefficient inverse problems for nonlinear reaction-diffusion-advection equations is proposed. As an example, we consider an inverse problem of restoring a coefficient in a nonlinear Burgers-type equation. One of the features of the inverse problem is a use of additional information about the position of a reaction front. Another feature of the approach is a use of asymptotic analysis methods to select a good initial guess in a gradient method for minimizing a cost functional that occurs when solving the coefficient inverse problem. Numerical experiments demonstrate the effectiveness of the proposed approach.

KW - Coefficient inverse problem

KW - Inverse problem with data on the position of a reaction front

KW - Reaction-diffusion-advection equation

KW - Singularly perturbed problem

UR - http://www.scopus.com/inward/record.url?scp=85103280953&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2021.105824

DO - 10.1016/j.cnsns.2021.105824

M3 - Article

AN - SCOPUS:85103280953

VL - 99

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

M1 - 105824

ER -

ID: 28256457