Approximate solution of the backward problem for Kirchhoff’s model of Parabolic type with discrete random noise

Abstract

In this paper, we consider the final boundary value problem for non-local Kirchhoff’s model of parabolic type with discrete random noise. We first discuss the instability of solutions. Then we present the regularized solution by the trigonometric method in non-parametric regression associated with the truncated expansion method. In addition, under a prior assumption on the exact solution, the convergence rate is obtained. In the last section, the effectiveness and suitability of our results are justified via numerical experiments.