Cauchy Problem of the Poisson Equation in a Multi-Connected Domain by a New Meshless Method

2021 ◽  
Vol 11 (05) ◽  
pp. 802-813
Author(s):  
珊珊 王
Keyword(s):  
Cauchy Problem ◽  
Poisson Equation ◽  
Connected Domain ◽  
Meshless Method ◽  
The Poisson Equation

scholarly journals Regularization and Error Estimate for the Poisson Equation with Discrete Data

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 422
Author(s):  
Nguyen Anh Triet ◽  
Nguyen Duc Phuong ◽  
Van Thinh Nguyen ◽  
Can Nguyen-Huu
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Poisson Equation ◽  
Regularization Method ◽  
Random Noise ◽  
Two Dimensional ◽  
The Poisson Equation ◽  
The Cauchy Problem ◽  
Ill Posed ◽  
Dimensional Domain

In this work, we focus on the Cauchy problem for the Poisson equation in the two dimensional domain, where the initial data is disturbed by random noise. In general, the problem is severely ill-posed in the sense of Hadamard, i.e., the solution does not depend continuously on the data. To regularize the instable solution of the problem, we have applied a nonparametric regression associated with the truncation method. Eventually, a numerical example has been carried out, the result shows that our regularization method is converged; and the error has been enhanced once the number of observation points is increased.

scholarly journals CARLEMAN'S FORMULA OF A SOLUTIONS OF THE POISSON EQUATION IN BOUNDED DOMAIN

2021 ◽  
Vol 7 (2) ◽  
pp. 110
Author(s):  
Ermamat N. Sattorov ◽  
Zuxro E. Ermamatova
Keyword(s):  
Cauchy Problem ◽  
Bounded Domain ◽  
Poisson Equation ◽  
Function Method ◽  
Normal Derivative ◽  
The Poisson Equation ◽  
The Cauchy Problem

We suggest an explicit continuation formula for a solution to the Cauchy problem for the Poisson equation in a domain from its values and values of its normal derivative on a part of the boundary. We construct the continuation formula of this problem based on the Carleman--Yarmuhamedov function method.

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