Application of Asymptotic Analysis for Solving the Inverse Problem of Determining the Coefficient of Linear Amplification in Burgers’ Equation

Abstract

Asymptotic analysis of a singularly perturbed reaction—diffusion—advection equation, which is called a Burgers-type equation in applications and has a solution with a sharp transition layer, is applied to solve the coefficient inverse problem of determining the coefficient of linear amplification from known information on the observed solution of the direct problem at the final moment of time. The efficiency of the approach proposed in this study is shown using a series of model numerical experiments.