scholarly journals The symmetry of minimizing harmonic maps from a two dimensional domain to the sphere

1993 ◽  
Vol 10 (5) ◽  
pp. 549-559 ◽  
Author(s):  
Étienne Sandier
Keyword(s):  
Harmonic Maps ◽  
Two Dimensional ◽  
Dimensional Domain

Nonlinear nonlocal problems for a parabolic equation in a two-dimensional domain

1997 ◽  
Vol 49 (2) ◽  
pp. 269-280
Author(s):  
Yu. A. Mitropol’skii ◽  
A. A. Berezovskii ◽  
M. Kh. Shkhanukov-Lafishev
Keyword(s):  
Parabolic Equation ◽  
Two Dimensional ◽  
Nonlocal Problems ◽  
Dimensional Domain

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.

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