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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

Abstract

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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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 20-31-70016.

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Correspondence to D. V. Lukyanenko.

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Translated by I. Ruzanova

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Argun, R.L., Gorbachev, A.V., Lukyanenko, D.V. et al. 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. Comput. Math. and Math. Phys. 62, 441–451 (2022). https://doi.org/10.1134/S0965542522030022

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Keywords:

  • inverse problem with data on the position of a reaction front
  • inverse boundary value problem
  • reaction–diffusion–advection equation