scholarly journals A Reaction-Diffusion System with Nonlinear Nonlocal Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Alexander Gladkov ◽  
Alexandr Nikitin
Keyword(s):  
Boundary Conditions ◽  
Nonlocal Boundary ◽  
Local Existence ◽  
Reaction Diffusion ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Initial Boundary Value

We consider initial boundary value problem for a reaction-diffusion system with nonlinear and nonlocal boundary conditions and nonnegative initial data. We prove local existence, uniqueness, and nonuniqueness of solutions.

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.

scholarly journals Blowup Properties for a Semilinear Reaction-Diffusion System with Nonlinear Nonlocal Boundary Conditions

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Dengming Liu ◽  
Chunlai Mu
Keyword(s):  
Boundary Condition ◽  
Global Existence ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Nonlocal Boundary Conditions ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Subsolution And Supersolution

We investigate the blowup properties of the positive solutions for a semilinear reaction-diffusion system with nonlinear nonlocal boundary condition. We obtain some sufficient conditions for global existence and blowup by utilizing the method of subsolution and supersolution.

scholarly journals On the stable difference scheme for the time delay telegraph equation

2020 ◽  
Vol 99 (3) ◽  
pp. 105-119
Author(s):  
A. Ashyralyev ◽  
◽  
K. Turk ◽  
D. Agirseven ◽  
◽  
...  
Keyword(s):  
Time Delay ◽  
Difference Scheme ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Telegraph Equation ◽  
Stability Estimates ◽  
The Difference ◽  
Initial Boundary Value

The stable difference scheme for the approximate solution of the initial boundary value problem for the telegraph equation with time delay in a Hilbert space is presented. The main theorem on stability of the difference scheme is established. In applications, stability estimates for the solution of difference schemes for the two type of the time delay telegraph equations are obtained. As a test problem, one-dimensional delay telegraph equation with nonlocal boundary conditions is considered. Numerical results are provided.

scholarly journals On the solvability of a mixed problem for a fractional partial differential equation with delayed time argument and Laplace operators with nonlocal boundary conditions in Sobolev classes

2020 ◽  
Vol 22 (1) ◽  
pp. 13-23
Author(s):  
Mahkambek M. Babayev
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Sobolev Classes ◽  
Laplace Operators ◽  
Partial Differential ◽  
Initial Boundary Value

In this paper, we study a problem with initial functions and boundary conditions for partial differential equations of fractional order with Laplace operators. The boundary conditions of the problem are nonlocal, and the solution is supposed to belong to one of Sobolev classes. The solution of the initial boundary value problem is constructed as the sum of a series of multidimensional spectral problem’s eigenfunctions. The eigenvalues of the spectral problem are found and the corresponding system of eigenfunctions is constructed. It is shown that this system is complete and forms a Riesz basis in the subspaces of Sobolev spaces. Basing on the completeness of the eigenfunctions’ system, the uniqueness theorem for the solution of the problem is proved. The existence of a regular solution of the initial boundary value problem is proved in Sobolev subspaces.

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