Determination of a time-dependent heat source under nonlocal boundary and integral overdetermination conditions

2011 ◽  
Vol 218 (8) ◽  
pp. 4138-4146 ◽  
Author(s):  
M.I. Ismailov ◽  
F. Kanca ◽  
D. Lesnic
Keyword(s):  
Heat Source ◽  
Nonlocal Boundary ◽  
Time Dependent ◽  
Integral Overdetermination

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.

scholarly journals Determination of a diffusion coefficient in a quasilinear parabolic equation

2017 ◽  
Vol 15 (1) ◽  
pp. 77-91 ◽  
Author(s):  
Fatma Kanca
Keyword(s):  
Diffusion Coefficient ◽  
Parabolic Equation ◽  
Numerical Experiments ◽  
Input Data ◽  
Quasilinear Parabolic Equation ◽  
Nonlocal Boundary ◽  
Time Dependent ◽  
Integral Overdetermination ◽  
Quasilinear Parabolic

Abstract This paper investigates the inverse problem of finding the time-dependent diffusion coefficient in a quasilinear parabolic equation with the nonlocal boundary and integral overdetermination conditions. 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. Finally, some numerical experiments are presented.

Identifying a time-dependent heat source with nonlocal boundary and overdetermination conditions by the variational iteration method

2014 ◽  
Vol 24 (7) ◽  
pp. 1545-1552 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu
Keyword(s):  
Exact Solution ◽  
Heat Source ◽  
Iteration Method ◽  
Numerical Technique ◽  
Nonlocal Boundary ◽  
Variational Iteration Method ◽  
Time Dependent ◽  
Successive Approximations ◽  
Content Type ◽  
Variational Iteration

Purpose – The purpose of this paper is to investigate the inverse problem of determining a time-dependent heat source in a parabolic equation with nonlocal boundary and integral overdetermination conditions. Design/methodology/approach – The variational iteration method (VIM) is employed as a numerical technique to develop numerical solution. A numerical example is presented to illustrate the advantages of the method. Findings – Using this method, we obtain the exact solution of this problem. Whether or not there is a noisy overdetermination data, our numerical results are stable. Thus the VIM is suitable for finding the approximation solution of the problem. Originality/value – This method is based on the use of Lagrange multipliers for the identification of optimal values of parameters in a functional and gives rapidly convergent successive approximations of the exact solution if such a solution exists.

BAYESIAN ESTIMATION OF A TIME DEPENDENT INTERNAL HEAT SOURCE IN A HETEROGENEOUS MEDIA

2016 ◽  
Author(s):  
Carolina Palma Naveira Cotta ◽  
Kelvin Chen ◽  
Christopher Tostado ◽  
Philippe Rollemberg d'Egmont ◽  
Fernando Duda ◽  
...  
Keyword(s):  
Heat Source ◽  
Bayesian Estimation ◽  
Heterogeneous Media ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Time Dependent
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