scholarly journals RADIAL SOLUTION OF ASYMPTOTICALLY LINEAR ELLIPTIC EQUATION WITH MIXED BOUNDARY VALUE IN ANNULAR DOMAIN

2020 ◽  
Vol 10 (6) ◽  
pp. 2787-2805
Author(s):  
Jian Tian ◽  
◽  
Yuanhong Wei
Keyword(s):  
Elliptic Equation ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Radial Solution ◽  
Annular Domain ◽  
Asymptotically Linear ◽  
Linear Elliptic Equation

scholarly journals The nonlocal boundary value problem with perturbations of mixed boundary conditions for an elliptic equation with constant coefficients. II

2020 ◽  
Vol 12 (1) ◽  
pp. 173-188
Author(s):  
Ya.O. Baranetskij ◽  
P.I. Kalenyuk ◽  
M.I. Kopach ◽  
A.V. Solomko
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Mixed Boundary Conditions ◽  
Multipoint Problem ◽  
Uniqueness Of The Solution

In this paper we continue to investigate the properties of the problem with nonlocal conditions, which are multipoint perturbations of mixed boundary conditions, started in the first part. In particular, we construct a generalized transform operator, which maps the solutions of the self-adjoint boundary-value problem with mixed boundary conditions to the solutions of the investigated multipoint problem. The system of root functions $V(L)$ of operator $L$ for multipoint problem is constructed. The conditions under which the system $V(L)$ is complete and minimal, and the conditions under which it is the Riesz basis are determined. In the case of an elliptic equation the conditions of existence and uniqueness of the solution for the problem are established.

scholarly journals On a method for approximate solution of a mixed boundary value problem for an elliptic equation

2021 ◽  
Vol 23 (1) ◽  
pp. 58-71
Author(s):  
Mahmut E. Fairuzov ◽  
Fedor V. Lubyshev
Keyword(s):  
Boundary Condition ◽  
Approximate Solution ◽  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Variable Coefficients ◽  
Natural Boundary Condition ◽  
Mixed Boundary Value Problem ◽  
Integration Region

A mixed boundary value problem for an elliptic equation of divergent type with variable coefficients is considered. It is assumed that the integration region is a rectangle, and the boundary of the integration region is the union of two disjoint pieces. The Dirichlet boundary condition is set on the first piece, and the Neumann boundary condition is set on the other one. The given problem is a problem with a discontinuous boundary condition. Such problems with mixed conditions at the boundary are most often encountered in practice in process modeling, and the methods for solving them are of considerable interest. This work is related to the paper [1] and complements it. It is focused on the approbation of the results established in [1] on the convergence of approximations of the original mixed boundary value problem with the main boundary condition of the third boundary value problem already with the natural boundary condition. On the basis of the results obtained in this paper and in [1], computational experiments on the approximate solution of model mixed boundary value problems are carried out.

Sign in / Sign up

Export Citation Format

Share Document