On well-posedness of source identification elliptic problem with nonlocal boundary conditions

2021 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Charyyar Ashyralyyev ◽  
Viktor G. Zvyagin
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problem ◽  
Source Identification ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Well Posedness

A Meshfree Computational Approach Based on Multiple-Scale Pascal Polynomials for Numerical Solution of a 2D Elliptic Problem with Nonlocal Boundary Conditions

2019 ◽  
Vol 17 (10) ◽  
pp. 1950080 ◽  
Author(s):  
Ömer Oruç
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problem ◽  
Numerical Solutions ◽  
Nonlocal Boundary ◽  
Meshfree Method ◽  
Multiple Scale ◽  
Nonlocal Boundary Conditions ◽  
Condition Numbers ◽  
Test Problems ◽  
Numerical Integrations

A two-dimensional (2D) elliptic problem with nonlocal boundary conditions on both regular and irregular domains is solved numerically by Pascal polynomial basis unified with multiple-scale technique. Very accurate numerical solutions and quite reasonable condition numbers are obtained with the proposed method which is also a truly meshfree method since difficult meshing processes or numerical integrations over domains are not needed for considered problems. Four test problems are solved to show the accuracy and efficiency of the proposed method. Also stability of the method is studied against large noise effect.

scholarly journals A 2.5D MODEL FOR THE EQUATIONS OF THE OCEAN AND THE ATMOSPHERE

2007 ◽  
Vol 05 (03) ◽  
pp. 199-229 ◽  
Author(s):  
Q. S. CHEN ◽  
J. LAMINIE ◽  
A. ROUSSEAU ◽  
R. TEMAM ◽  
J. TRIBBIA
Keyword(s):  
Boundary Conditions ◽  
Constant Velocity ◽  
Degrees Of Freedom ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Primitive Equations ◽  
Well Posedness ◽  
Related Model ◽  
Nonhomogeneous Boundary ◽  
Nonhomogeneous Boundary Conditions

The primitive equations (PEs) of the atmosphere and the ocean without viscosity are considered. A 2.5D model is introduced, whose motivation is described in the Introduction. A set of nonlocal boundary conditions is proposed, and well-posedness is established for the flows linearized around a constant velocity stratified flow; homogeneous and nonhomogeneous boundary conditions are considered. A related model of dimension 2.5, of physical interest but with fewer degrees of freedom, is also considered at the end.

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Jiang ◽  
Zhong Chen ◽  
Ning Hu ◽  
Yali Chen
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Reproducing Kernel ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Orthonormal Bases ◽  
Fractional Differential

AbstractIn recent years, the study of fractional differential equations has become a hot spot. It is more difficult to solve fractional differential equations with nonlocal boundary conditions. In this article, we propose a multiscale orthonormal bases collocation method for linear fractional-order nonlocal boundary value problems. In algorithm construction, the solution is expanded by the multiscale orthonormal bases of a reproducing kernel space. The nonlocal boundary conditions are transformed into operator equations, which are involved in finding the collocation coefficients as constrain conditions. In theory, the convergent order and stability analysis of the proposed method are presented rigorously. Finally, numerical examples show the stability, accuracy and effectiveness of the method.

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