Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation

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Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation. / Lukyanenko, Dmitry V.; Shishlenin, Maxim A.; Volkov, Vladimir T.

In: Journal of Inverse and Ill-Posed Problems, Vol. 27, No. 5, 10.2019, p. 745-758.

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

BibTeX

@article{9ac50b68f86444bcb6e57a4b75eeddb8,

title = "Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation",

abstract = "In this paper, a new asymptotic-numerical approach to solving an inverse boundary value problem for a nonlinear singularly perturbed parabolic equation with time-periodic coefficients is proposed. An unknown boundary condition is reconstructed by using known additional information about the location of a moving front. An asymptotic analysis of the direct problem allows us to reduce the original inverse problem to that with a simpler numerical solution. Numerical examples demonstrate the efficiency of the method.",

keywords = "interior layers, Inverse boundary value problem, numerical method, reaction-diffusion-advection equation, singularly perturbed problem, LEVITAN, KREIN, RECONSTRUCTION, ALGORITHM, MODEL, NUMERICAL-SOLUTION, COEFFICIENT, GELFAND",

author = "Lukyanenko, {Dmitry V.} and Shishlenin, {Maxim A.} and Volkov, {Vladimir T.}",

year = "2019",

month = oct,

doi = "10.1515/jiip-2017-0074",

language = "English",

volume = "27",

pages = "745--758",

journal = "Journal of Inverse and Ill-Posed Problems",

issn = "0928-0219",

publisher = "Walter de Gruyter GmbH",

number = "5",

}

RIS

TY - JOUR

T1 - Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation

AU - Lukyanenko, Dmitry V.

AU - Shishlenin, Maxim A.

AU - Volkov, Vladimir T.

PY - 2019/10

Y1 - 2019/10

N2 - In this paper, a new asymptotic-numerical approach to solving an inverse boundary value problem for a nonlinear singularly perturbed parabolic equation with time-periodic coefficients is proposed. An unknown boundary condition is reconstructed by using known additional information about the location of a moving front. An asymptotic analysis of the direct problem allows us to reduce the original inverse problem to that with a simpler numerical solution. Numerical examples demonstrate the efficiency of the method.

AB - In this paper, a new asymptotic-numerical approach to solving an inverse boundary value problem for a nonlinear singularly perturbed parabolic equation with time-periodic coefficients is proposed. An unknown boundary condition is reconstructed by using known additional information about the location of a moving front. An asymptotic analysis of the direct problem allows us to reduce the original inverse problem to that with a simpler numerical solution. Numerical examples demonstrate the efficiency of the method.

KW - interior layers

KW - Inverse boundary value problem

KW - numerical method

KW - reaction-diffusion-advection equation

KW - singularly perturbed problem

KW - LEVITAN

KW - KREIN

KW - RECONSTRUCTION

KW - ALGORITHM

KW - MODEL

KW - NUMERICAL-SOLUTION

KW - COEFFICIENT

KW - GELFAND

UR - http://www.scopus.com/inward/record.url?scp=85069764054&partnerID=8YFLogxK

U2 - 10.1515/jiip-2017-0074

DO - 10.1515/jiip-2017-0074

M3 - Article

AN - SCOPUS:85069764054

VL - 27

SP - 745

EP - 758

JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

SN - 0928-0219

IS - 5

ER -

ID: 21045044