Approximate solution of the backward problem for Kirchhoff's model of Parabolic type with discrete random noise. (1st August 2020)

• Record Type: Journal Article
• Authors: Triet, Nguyen Anh; Phuong, Nguyen Duc; O'Regan, Donal; Tuan, Nguyen Huy
• Is Part Of: Computers & mathematics with applications. Volume 80:issue 3(2020)
• Page Start: 453
• Page End: 470
• Publication Date: 2020-08-01
• Subjects: Kirchhoff's model -- Ill-posed problem -- Random noise -- Regularized solution; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.03.015
• Languages: English
• ISSNs: 0898-1221

Abstract

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.