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

Authors: Nguyễn Anh Triết, Nguyen Duc Phuong, Nguyễn Huy Tuấn, Donal O'Regan, Nguyễn Huy Tuấn, Donal O’Regan,

https://doi.org/10.1016/j.camwa.2020.03.015

Publisher, magazine: ,

Publication year: 2020

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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.

Tags: Kirchhoff’s model, Ill-posed problem, Random noise, Regularized solution