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.

scholarly journals INVERSE PROBLEM OF A ONE-DIMENSIONAL MODEL IN MULTILAYER HEAT CONDUCTION

2020 ◽  
Vol 19 (1) ◽  
pp. 42
Author(s):  
G. C. Oliveira ◽  
S. S. Ribeiroa ◽  
G. Guimarães
Keyword(s):  
Inverse Problem ◽  
Measurement Errors ◽  
Input Data ◽  
Temperature Measurements ◽  
Dimensional Model ◽  
One Dimensional ◽  
Ill Posed ◽  
Measurements Errors ◽  
Chip Chip

The inverse problem in conducting heat is related to the determination of the boundary condition, rate of heat generation, or thermophysical properties, using temperature measurements at one or more positions of the solid. The inverse problem in conducting heat is mathematically one of the ill-posed problems, because its solution extremely sensitive to measurement errors. For a well-placed problem the following conditions must be satisfied: the solution must exist, it must be unique and must be stable on small changes of the input data. The objective of the work is to estimate the heat flux generated at the tool-chip-chip interface in a manufacturing process. The term "estimation" is used because in the temperature measurements, errors are always present and these affect the accuracy of the calculation of the heat flow.

scholarly journals Constructing a basis from systems of eigenfunctions of one not strengthened regular boundary value problem

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 981-987 ◽  
Author(s):  
Makhmud Sadybekov ◽  
Gulnara Dildabek ◽  
Aizhan Tengayeva
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Fourier Method ◽  
Regular Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Variable Separation ◽  
Stationary Diffusion ◽  
New System

We investigate a nonlocal boundary value spectral problem for an ordinary differential equation in an interval. Such problems arise in solving the nonlocal boundary value problem for partial equations by the Fourier method of variable separation. For example, they arise in solving nonstationary problems of diffusion with boundary conditions of Samarskii-Ionkin type. Or they arise in solving problems with stationary diffusion with opposite flows on a part of the interval. The boundary conditions of this problem are regular but not strengthened regular. The principal difference of this problem is: the system of eigenfunctions is comlplete but not forming a basis. Therefore the direct applying of the Fourier method is impossible. Based on these eigenfunctions there is constructed a special system of functions that already forms the basis. However the obtained system is not already the system of the eigenfunctions of the problem. We demonstrate how this new system of functions can be used for solving a nonlocal boundary value problem on the example of the Laplace equation.

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