scholarly journals A new ADI technique for two-dimensional parabolic equation with an integral condition

2002 ◽  
Vol 43 (12) ◽  
pp. 1477-1488 ◽  
Author(s):  
M. Dehghan
Keyword(s):  
Parabolic Equation ◽  
Integral Condition ◽  
Two Dimensional

scholarly journals Alternating direction method for two-dimensional parabolic equation with nonlocal integral condition

2012 ◽  
Vol 17 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Mifodijus Sapagovas ◽  
Kristina Jakubėlienė
Keyword(s):  
Parabolic Equation ◽  
Nonlocal Condition ◽  
Integral Condition ◽  
Rectangular Domain ◽  
Alternating Direction Method ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Alternating Direction ◽  
Nonlocal Integral Condition ◽  
Dimensional Domain

Two-dimensional parabolic equation with nonlocal condition is solved by alternating direction method in the rectangular domain. Values of the solution on the boundary points are bind with the integral of the solution in whole two-dimensional domain. Because of this nonlocal condition, the classical alternating direction method is complemented by the solution of low dimension system of algebraic equations. The peculiarities of the method are considered.

scholarly journals An eigenvalue problem for the differential operator with an integral condition

2012 ◽  
Vol 53 ◽  
Author(s):  
Kristina Jakubėlienė
Keyword(s):  
Parabolic Equation ◽  
Differential Operator ◽  
Eigenvalue Problem ◽  
Integral Condition ◽  
Stability Conditions ◽  
Two Dimensional ◽  
One Dimensional ◽  
Nonlocal Integral Condition

We analyze solution of a two-dimensional parabolic equation with a nonlocal integral condition by a locally one-dimensional method. The main aim of the paper is to deduce stability conditions of a system of one-dimensional equations with one integral condition. To this end, we analyze the structure of the spectrum of the differential operator with an integral condition.

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

On a Nonlocal Boundary-value Problem for Two-dimensional Elliptic Equation

2001 ◽  
Vol 3 (1) ◽  
pp. 62-71
Author(s):  
Givi Berikelashvili ◽  
Nikolai I. Ionkin ◽  
Valentina A. Morozova
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Weighted Sobolev Space ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Condition ◽  
Two Dimensional ◽  
Averaging Operators ◽  
Nonlocal Integral Condition ◽  
Constant Coefficients

AbstractA boundary-value problem with a nonlocal integral condition is considered for a two-dimensional elliptic equation with constant coefficients and a mixed derivative. The existence and uniqueness of a weak solution of this problem are proved in a weighted Sobolev space. A difference scheme is constructed using the Steklov averaging operators.

scholarly journals An inverse source problem for a two dimensional time fractional diffusion equation with involution

2021 ◽  
Author(s):  
Batirkhan Turmetov ◽  
B. J. Kadirkulov
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Diffusion Equation ◽  
Fourier Method ◽  
Dirichlet Condition ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Inverse Source Problem ◽  
Two Dimensional ◽  
Time Fractional Diffusion Equation

In this paper, we consider a two-dimensional generalization of the parabolic equation. Using the Fourier method, we study the solvability of the inverse problem with the Dirichlet condition and periodic conditions.

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