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 |
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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. |
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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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