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Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data. / Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 54, 01.01.2018, p. 233-247.

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

Harvard

Lukyanenko, DV, Shishlenin, MA & Volkov, VT 2018, 'Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data', Communications in Nonlinear Science and Numerical Simulation, vol. 54, pp. 233-247. https://doi.org/10.1016/j.cnsns.2017.06.002

APA

Lukyanenko, D. V., Shishlenin, M. A., & Volkov, V. T. (2018). Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data. Communications in Nonlinear Science and Numerical Simulation, 54, 233-247. https://doi.org/10.1016/j.cnsns.2017.06.002

Vancouver

Lukyanenko DV, Shishlenin MA, Volkov VT. Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data. Communications in Nonlinear Science and Numerical Simulation. 2018 Jan 1;54:233-247. doi: 10.1016/j.cnsns.2017.06.002

Author

Lukyanenko, D. V. ; Shishlenin, M. A. ; Volkov, V. T. / Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data. In: Communications in Nonlinear Science and Numerical Simulation. 2018 ; Vol. 54. pp. 233-247.

BibTeX

@article{fb709edfd8ef4be9bd2d9560684b7268,
title = "Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data",
abstract = "We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.",
keywords = "Coefficient inverse problem, Dynamically adapted mesh, Final time observed data, Interior and boundary layers, Reaction-diffusion-advection equation, Singularly perturbed problem, BURGERS-EQUATION",
author = "Lukyanenko, {D. V.} and Shishlenin, {M. A.} and Volkov, {V. T.}",
year = "2018",
month = jan,
day = "1",
doi = "10.1016/j.cnsns.2017.06.002",
language = "English",
volume = "54",
pages = "233--247",
journal = "Communications in Nonlinear Science and Numerical Simulation",
issn = "1007-5704",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

AU - Lukyanenko, D. V.

AU - Shishlenin, M. A.

AU - Volkov, V. T.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

AB - We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

KW - Coefficient inverse problem

KW - Dynamically adapted mesh

KW - Final time observed data

KW - Interior and boundary layers

KW - Reaction-diffusion-advection equation

KW - Singularly perturbed problem

KW - BURGERS-EQUATION

UR - http://www.scopus.com/inward/record.url?scp=85020420501&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2017.06.002

DO - 10.1016/j.cnsns.2017.06.002

M3 - Article

AN - SCOPUS:85020420501

VL - 54

SP - 233

EP - 247

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

ER -

ID: 12100575