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Regularized solution for nonlinear elliptic equations with random discrete data

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2019

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Wiley

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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.

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Ill-Posed Problem, Nonlinear Elliptic, Random Noise, Regularized Solution

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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.

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Mathematical Methods in the Applied Sciences

Volume

42

Issue

18

Start Page

6829

End Page

6848