Determination of a time-dependent heat source from nonlocal boundary conditions

2013 ◽  
Vol 37 (6) ◽  
pp. 936-956 ◽  
Author(s):  
A. Hazanee ◽  
D. Lesnic
Keyword(s):  
Heat Source ◽  
Boundary Conditions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Time Dependent

scholarly journals Determination of a time-dependent heat source under not strengthened regular boundary and integral overdetermination conditions

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 809-814 ◽  
Author(s):  
Makhmud Sadybekov ◽  
Gulaiym Oralsyn ◽  
Mansur Ismailov
Keyword(s):  
Inverse Problem ◽  
Heat Source ◽  
Input Data ◽  
Nonlocal Boundary ◽  
Fourier Method ◽  
Time Dependent ◽  
Regular Boundary ◽  
Associated Functions ◽  
Integral Overdetermination

We investigate an inverse problem of finding a time-dependent heat source in a parabolic equation with nonlocal boundary and integral overdetermination conditions. The boundary conditions of this problem are regular but not strengthened regular. The principal difference of this problem is: the system of eigenfunctions is not complete. But the system of eigen- and associated functions forming a basis. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown by using the generalized Fourier method.

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.

Sign in / Sign up

Export Citation Format

Share Document