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Num. Meth. Prog., 2019, Volume 20, Issue 4, Pages 363–377 (Mi vmp973)  

Application of asymptotic analysis methods for solving a coefficient inverse problem for a system of nonlinear singularly perturbed reaction-diffusion equations with cubic nonlinearity

D. V. Lukyanenko, A. A. Mel'nikova

Faculty of Physics, Lomonosov Moscow State University

Abstract: The capabilities of asymptotic analysis methods for solving a coefficient inverse problem for a system of nonlinear singularly perturbed equations of reaction-diffusion type with cubic nonlinearity are shown. The problem considered for a system of partial differential equations is reduced to a system of algebraic equations that is much simpler for a numerical study and relates the data of the inverse problem (the information on the position of the reaction front in time) with the coefficient to be recovered. Numerical results confirm the efficiency of the proposed approach.

Keywords: singularly perturbed problem, interior and boundary layers, reaction-diffusion equation, inverse problem with the location of moving front data.

DOI: https://doi.org/10.26089/NumMet.v20r432

Full text: PDF file (660 kB)

UDC: 519.6
Received: 11.08.2019

Citation: D. V. Lukyanenko, A. A. Mel'nikova, “Application of asymptotic analysis methods for solving a coefficient inverse problem for a system of nonlinear singularly perturbed reaction-diffusion equations with cubic nonlinearity”, Num. Meth. Prog., 20:4 (2019), 363–377

Citation in format AMSBIB
\Bibitem{LukMel19}
\by D.~V.~Lukyanenko, A.~A.~Mel'nikova
\paper Application of asymptotic analysis methods for solving a coefficient inverse problem for a system of nonlinear singularly perturbed reaction-diffusion equations with cubic nonlinearity
\jour Num. Meth. Prog.
\yr 2019
\vol 20
\issue 4
\pages 363--377
\mathnet{http://mi.mathnet.ru/vmp973}
\crossref{https://doi.org/10.26089/NumMet.v20r432}


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