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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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
Singularly perturbed problem
Interior and boundary layers
Reaction–diffusion–advection equation

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The work was supported by RFBR, Russia (Project Nos. 18-01-00865, 18-31-00204, 16-01-00755 and 17-01-00159).