Solving of the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction–diffusion equation with the location of moving front data

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Solving of the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction–diffusion equation with the location of moving front data. / Lukyanenko, D. V.; Grigorev, V. B.; Volkov, V. T. et al.

In: Computers and Mathematics with Applications, Vol. 77, No. 5, 01.03.2019, p. 1245-1254.

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

BibTeX

@article{be8dfa0913154d978417e14406dec683,

title = "Solving of the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction–diffusion equation with the location of moving front data",

abstract = "Asymptotic-numerical approach to solving the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction–diffusion equation by knowing the location of moving front data is proposed. Asymptotic analysis of the direct problem allows to reduce the original two-dimensional parabolic problem to a series of more simple equations with lower dimension for the determination of moving front parameters. It enables to associate the observed location of the moving front to the parameters which have to be identified. Numerical examples show the effectiveness of the proposed method.",

keywords = "Coefficient inverse problem, Interior and boundary layers, Reaction–diffusion–advection equation, Singularly perturbed problem, LEVITAN, KREIN, RECONSTRUCTION, ALGORITHM, GELFAND, Reaction-diffusion-advection equation, BOUNDARY CONTROL",

author = "Lukyanenko, {D. V.} and Grigorev, {V. B.} and Volkov, {V. T.} and Shishlenin, {M. A.}",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Ltd",

year = "2019",

month = mar,

day = "1",

doi = "10.1016/j.camwa.2018.11.005",

language = "English",

volume = "77",

pages = "1245--1254",

journal = "Computers and Mathematics with Applications",

issn = "0898-1221",

publisher = "Elsevier Ltd",

number = "5",

}

RIS

TY - JOUR

T1 - Solving of the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction–diffusion equation with the location of moving front data

AU - Lukyanenko, D. V.

AU - Grigorev, V. B.

AU - Volkov, V. T.

AU - Shishlenin, M. A.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - Asymptotic-numerical approach to solving the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction–diffusion equation by knowing the location of moving front data is proposed. Asymptotic analysis of the direct problem allows to reduce the original two-dimensional parabolic problem to a series of more simple equations with lower dimension for the determination of moving front parameters. It enables to associate the observed location of the moving front to the parameters which have to be identified. Numerical examples show the effectiveness of the proposed method.

AB - Asymptotic-numerical approach to solving the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction–diffusion equation by knowing the location of moving front data is proposed. Asymptotic analysis of the direct problem allows to reduce the original two-dimensional parabolic problem to a series of more simple equations with lower dimension for the determination of moving front parameters. It enables to associate the observed location of the moving front to the parameters which have to be identified. Numerical examples show the effectiveness of the proposed method.

KW - Coefficient inverse problem

KW - Interior and boundary layers

KW - Reaction–diffusion–advection equation

KW - Singularly perturbed problem

KW - LEVITAN

KW - KREIN

KW - RECONSTRUCTION

KW - ALGORITHM

KW - GELFAND

KW - Reaction-diffusion-advection equation

KW - BOUNDARY CONTROL

UR - http://www.scopus.com/inward/record.url?scp=85056841440&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2018.11.005

DO - 10.1016/j.camwa.2018.11.005

M3 - Article

AN - SCOPUS:85056841440

VL - 77

SP - 1245

EP - 1254

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 5

ER -

ID: 17509377