Features of Numerical Reconstruction of a Boundary Condition in an Inverse Problem for a Reaction–Diffusion–Advection Equation with Data on the Position of a Reaction Front

A new approach to the reconstruction of a boundary condition in an inverse problem for a nonlinear singularly perturbed reaction–diffusion–advection equation with data on the reaction front position is proposed. The problem is solved via gradient minimization of a cost functional with an initial app...

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Veröffentlicht in:Computational mathematics and mathematical physics 2022-03, Vol.62 (3), p.441-451
Hauptverfasser: Argun, R. L., Gorbachev, A. V., Lukyanenko, D. V., Shishlenin, M. A.
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container_title Computational mathematics and mathematical physics
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creator Argun, R. L.
Gorbachev, A. V.
Lukyanenko, D. V.
Shishlenin, M. A.
description A new approach to the reconstruction of a boundary condition in an inverse problem for a nonlinear singularly perturbed reaction–diffusion–advection equation with data on the reaction front position is proposed. The problem is solved via gradient minimization of a cost functional with an initial approximation chosen by applying asymptotic analysis methods. The efficiency of the proposed approach is demonstrated by numerical experiments.
doi_str_mv 10.1134/S0965542522030022
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subjects Advection
Advection-diffusion equation
Asymptotic methods
Boundary conditions
Computational Mathematics and Numerical Analysis
Cost analysis
Inverse problems
Mathematical Physics
Mathematics
Mathematics and Statistics
Reconstruction
title Features of Numerical Reconstruction of a Boundary Condition in an Inverse Problem for a Reaction–Diffusion–Advection Equation with Data on the Position of a Reaction Front
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