Effective Approximation for Elliptic Partial Differential Equation with Periodical Boundary Value Problem

2010 ◽  
Vol 29-32 ◽  
pp. 1294-1300
Author(s):  
Xin Cai
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Elliptic Partial Differential Equation ◽  
Partial Differential ◽  
Layer Function ◽  
Smooth Component ◽  
Boundary Layer Function

Elliptic partial differential equation with periodical boundary value problem was considered. The equation would degenerate to parabolic partial differential equation when small parameter tends to zero. This is a multi-scale problem. Firstly, the property of boundary layer was discussed. Secondly, the boundary layer function was presented. The smooth component was constructed according to the boundary layer function. Thirdly, finite difference scheme for the smooth component is proposed according to transition point in time direction. Finally, experiment was proposed to illustrate that our presented method is an effective computational method.

scholarly journals Comparison results for nonlinear divergence structure elliptic PDE’s

2019 ◽  
Vol 9 (1) ◽  
pp. 438-448 ◽  
Author(s):  
Yichen Liu ◽  
Monica Marras ◽  
Giovanni Porru
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Elliptic Partial Differential Equation ◽  
Comparison Result ◽  
Partial Differential ◽  
Laplace Equations ◽  
Comparison Results ◽  
Divergence Structure

Abstract First we prove a comparison result for a nonlinear divergence structure elliptic partial differential equation. Next we find an estimate of the solution of a boundary value problem in a domain Ω in terms of the solution of a related symmetric boundary value problem in a ball B having the same measure as Ω. For p-Laplace equations, the corresponding result is due to Giorgio Talenti. In a special (radial) case we also prove a reverse comparison result.

scholarly journals A note on the nonlocal boundary value problem for a third order partial differential equation

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 801-808 ◽  
Author(s):  
Kh. Belakroum ◽  
A. Ashyralyev ◽  
A. Guezane-Lakoud
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Order Partial Differential Equation ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Partial Differential

The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space with a self-adjoint positive definite operator is considered. Applying operator approach, the theorem on stability for solution of this nonlocal boundary value problem is established. In applications, the stability estimates for the solution of three nonlocal boundary value problems for third order partial differential equations are obtained.

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