Regularized solution for nonlinear elliptic equations with random discrete data
No Thumbnail Available
Date
2019
Journal Title
Journal ISSN
Volume Title
Publisher
Wiley
Open Access Color
OpenAIRE Downloads
OpenAIRE Views
Abstract
The aim of this paper is to study the Cauchy problem of determining a solution of nonlinear elliptic equations with random discrete data. A study showing that this problem is severely ill posed in the sense of Hadamard, ie, the solution does not depend continuously on the initial data. It is therefore necessary to regularize the in-stable solution of the problem. First, we use the trigonometric of nonparametric regression associated with the truncation method in order to offer the regularized solution. Then, under some presumption on the true solution, we give errors estimates and convergence rate in L-2-norm. A numerical example is also constructed to illustrate the main results.
Description
Keywords
Ill-Posed Problem, Nonlinear Elliptic, Random Noise, Regularized Solution
Turkish CoHE Thesis Center URL
Fields of Science
Citation
Nguyen Duc Phuong; Nguyen Huy Tuan...et al. (2019). "Regularized solution for nonlinear elliptic equations with random discrete data", Mathematical Methods in the Applied Sciences, Vol. 42, No. 18, pp. 6829-6848.
WoS Q
Scopus Q
Source
Mathematical Methods in the Applied Sciences
Volume
42
Issue
18
Start Page
6829
End Page
6848