TY - JOUR

T1 - Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation

AU - Lukyanenko, Dmitry V.

AU - Shishlenin, Maxim A.

AU - Volkov, Vladimir T.

PY - 2019/10

Y1 - 2019/10

N2 - 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.

AB - 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.

KW - interior layers

KW - Inverse boundary value problem

KW - numerical method

KW - reaction-diffusion-advection equation

KW - singularly perturbed problem

KW - LEVITAN

KW - KREIN

KW - RECONSTRUCTION

KW - ALGORITHM

KW - MODEL

KW - NUMERICAL-SOLUTION

KW - COEFFICIENT

KW - GELFAND

UR - http://www.scopus.com/inward/record.url?scp=85069764054&partnerID=8YFLogxK

U2 - 10.1515/jiip-2017-0074

DO - 10.1515/jiip-2017-0074

M3 - Article

AN - SCOPUS:85069764054

VL - 27

SP - 745

EP - 758

JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

SN - 0928-0219

IS - 5

ER -