scholarly journals Identifying the heat sink

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
J. D. Audu ◽  
A. Boumenir ◽  
K. M. Furati ◽  
I. O. Sarumi
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Temperature Profile ◽  
Spectral Methods ◽  
Heat Sink ◽  
Evolution Equations ◽  
Identification Problem ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Pseudo Spectral

<p style='text-indent:20px;'>In this paper we examine the identification problem of the heat sink for a one dimensional heat equation through observations of the solution at the boundary or through a desired temperature profile to be attained at a certain given time. We make use of pseudo-spectral methods to recast the direct as well as the inverse problem in terms of linear systems in matrix form. The resulting evolution equations in finite dimensional spaces leads to fast real time algorithms which are crucial to applied control theory.</p>

Inversion of the Initial Value for a Time-Fractional Diffusion-Wave Equation by Boundary Data

2020 ◽  
Vol 20 (1) ◽  
pp. 109-120 ◽  
Author(s):  
Suzhen Jiang ◽  
Kaifang Liao ◽  
Ting Wei
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Fractional Diffusion ◽  
Initial Value ◽  
Diffusion Wave ◽  
One Dimensional ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
Continuation Technique

AbstractIn this study, we consider an inverse problem of recovering the initial value for a multi-dimensional time-fractional diffusion-wave equation. By using some additional boundary measured data, the uniqueness of the inverse initial value problem is proven by the Laplace transformation and the analytic continuation technique. The inverse problem is formulated to solve a Tikhonov-type optimization problem by using a finite-dimensional approximation. We test four numerical examples in one-dimensional and two-dimensional cases for verifying the effectiveness of the proposed algorithm.

scholarly journals A Note on the Right-Hand Side Identification Problem Arising in Biofluid Mechanics

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Abdullah Said Erdogan
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Identification Problem ◽  
Well Posedness ◽  
Space Operator ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Right Hand ◽  
Variable Space ◽  
The Right

The inverse problem of reconstructing the right-hand side (RHS) of a mixed problem for one-dimensional diffusion equation with variable space operator is considered. The well-posedness of this problem in Hölder spaces is established.

scholarly journals Feedback exponential stabilization of the semilinear heat equation with nonlocal initial conditions

2021 ◽  
Vol 26 (6) ◽  
pp. 1106-1122
Author(s):  
Ionuţ Munteanu
Keyword(s):  
Heat Equation ◽  
Closed Loop ◽  
Initial Conditions ◽  
Dimensional Structure ◽  
One Dimensional ◽  
Loop Equation ◽  
Nonlocal Initial Conditions ◽  
Semilinear Heat Equation ◽  
Finite Dimensional ◽  
The One

The present paper is devoted to the problem of stabilization of the one-dimensional semilinear heat equation with nonlocal initial conditions. The control is with boundary actuation. It is linear, of finite-dimensional structure, given in an explicit form. It allows to write the corresponding solution of the closed-loop equation in a mild formulation via a kernel, then to apply a fixed point argument in a convenient space.

A linear regularization method for a parameter identification problem in heat equation

2020 ◽  
Vol 28 (2) ◽  
pp. 251-273
Author(s):  
Subhankar Mondal ◽  
M. Thamban Nair
Keyword(s):  
Heat Equation ◽  
Parameter Identification ◽  
Regularization Method ◽  
Identification Problem ◽  
Practical Application ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Choice Strategy ◽  
Parameter Identification Problem ◽  
Parameter Choice Strategy

AbstractRecently, Nair and Roy (2017) considered a linear regularization method for a parameter identification problem in an elliptic PDE. In this paper, we consider similar procedure for identifying the diffusion coefficient in the heat equation, modifying the Sobolev spaces involved appropriately. We derive error estimates under appropriate conditions and also consider the finite-dimensional realization of the method, which is essential for practical application. In the analysis of finite-dimensional realization, we give a procedure to obtain finite-dimensional subspaces of an infinite-dimensional Hilbert space {L^{2}(0,T;H^{1}(\Omega))} by doing double discretization, that is, discretization corresponding to both the space and time domain. Also, we analyze the parameter choice strategy and obtain an a posteriori parameter which is order optimal.

scholarly journals An iterative method to calculate the thermal characteristics of the rock mass with inaccurate initial data

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Bolatbek Rysbaiuly ◽  
Nadiya Yunicheva ◽  
Nazerke Rysbayeva
Keyword(s):  
Inverse Problem ◽  
Rock Mass ◽  
Initial Data ◽  
Iterative Method ◽  
Heat Equation ◽  
Thermal Characteristics ◽  
Coefficient Inverse Problem ◽  
Difference Problem ◽  
One Dimensional ◽  
Interval Width

Abstract The paper discusses the coefficient inverse problem for one-dimensional heat equation with inaccurate initial data. A conjugate difference problem is developed on difference level. The problem is solved by method of interval analysis. Condition of applicability of Thomas method and its computational convergence are obtained. Estimates of the interval width of solutions of difference problems and functions of Thomas method are also gained.

Pseudo-spectral methods in one-dimensional magnetostriction

Meccanica ◽  
2014 ◽  
Vol 50 (1) ◽  
pp. 99-108 ◽  
Author(s):  
Andrea Nobili ◽  
Angelo Marcello Tarantino
Keyword(s):  
Spectral Methods ◽  
One Dimensional ◽  
Pseudo Spectral

AN INVERSE PROBLEM FOR THE HYPERBOLIC HEAT EQUATION

1992 ◽  
Vol 02 (01) ◽  
pp. 113-120
Author(s):  
E.G. SAVATEEV ◽  
L.M. DE SOCIO
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
One Dimensional ◽  
Constructive Solution ◽  
Local Existence And Uniqueness ◽  
Diffusive Term ◽  
Hyperbolic Heat Equation

In this paper we prove a theorem of local existence and uniqueness for the solution of the hyperbolic heat equation in the case where the coefficient of the diffusive term is unknown. The problem is one-dimensional in space and the ratio of the two characteristics times, upon which the physics depends, is small. The demonstration relies on a constructive solution.

scholarly journals Linear evolution equations on the half-line with dynamic boundary conditions

2021 ◽  
pp. 1-33
Author(s):  
D. A. SMITH ◽  
W. Y. TOH
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Evolution Equations ◽  
Half Line ◽  
Robin Problem ◽  
Dynamic Boundary Conditions ◽  
Transform Method ◽  
Linear Evolution ◽  
Robin Condition ◽  
Linear Evolution Equations

The classical half-line Robin problem for the heat equation may be solved via a spatial Fourier transform method. In this work, we study the problem in which the static Robin condition $$bq(0,t) + {q_x}(0,t) = 0$$ is replaced with a dynamic Robin condition; $$b = b(t)$$ is allowed to vary in time. Applications include convective heating by a corrosive liquid. We present a solution representation and justify its validity, via an extension of the Fokas transform method. We show how to reduce the problem to a variable coefficient fractional linear ordinary differential equation for the Dirichlet boundary value. We implement the fractional Frobenius method to solve this equation and justify that the error in the approximate solution of the original problem converges appropriately. We also demonstrate an argument for existence and unicity of solutions to the original dynamic Robin problem for the heat equation. Finally, we extend these results to linear evolution equations of arbitrary spatial order on the half-line, with arbitrary linear dynamic boundary conditions.

Sign in / Sign up

Export Citation Format

Share Document