Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation

Dmitry V. Lukyanenko, Maxim A. Shishlenin, Vladimir T. Volkov

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

In this paper, a new asymptotic-numerical approach to solving an inverse boundary value problem for a nonlinear singularly perturbed parabolic equation with time-periodic coefficients is proposed. An unknown boundary condition is reconstructed by using known additional information about the location of a moving front. An asymptotic analysis of the direct problem allows us to reduce the original inverse problem to that with a simpler numerical solution. Numerical examples demonstrate the efficiency of the method.

Original languageEnglish
Pages (from-to)745-758
Number of pages14
JournalJournal of Inverse and Ill-Posed Problems
Volume27
Issue number5
DOIs
Publication statusPublished - Oct 2019

Keywords

  • interior layers
  • Inverse boundary value problem
  • numerical method
  • reaction-diffusion-advection equation
  • singularly perturbed problem
  • LEVITAN
  • KREIN
  • RECONSTRUCTION
  • ALGORITHM
  • MODEL
  • NUMERICAL-SOLUTION
  • COEFFICIENT
  • GELFAND

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