Investigation of the Initial Inverse Problem in the Heat Equation

2004 ◽  
Vol 126 (2) ◽  
pp. 294-296 ◽  
Author(s):  
Khalid Masood ◽  
F. D. Zaman
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Heat Equation ◽  
Initial Temperature ◽  
Final Temperature ◽  
Conduction Model ◽  
Heat Conduction Model ◽  
Ill Posed

We investigate the inverse problem in the heat equation involving the recovery of the initial temperature from measurements of the final temperature. This problem is extremely ill-posed and it is believed that only information in the first few modes can be recovered by classical methods. We will consider this problem with a regularizing parameter which approximates and regularizes the heat conduction model.

A smoothing spline-based regularization of the initial inverse problem in a two-dimensional heat equation

2008 ◽  
Vol 223 (2) ◽  
pp. 439-449 ◽  
Author(s):  
K Masood ◽  
M T Mustafa
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Temperature Distribution ◽  
Smoothing Splines ◽  
Smoothing Spline ◽  
Hyperbolic Heat Conduction ◽  
Parabolic Model ◽  
Initial Profile ◽  
Conduction Model ◽  
Heat Conduction Model

A smoothing spline-based method and a hyperbolic heat conduction model is applied to regularize the recovery of the initial profile from a parabolic heat conduction model in two-dimensions. An ill-posed inverse problem involving recovery of the initial temperature distribution from measurements of the final temperature distribution is investigated. A hyperbolic heat conduction model is considered instead of a parabolic model and smoothing splines are applied to regularize the recovered initial profile. The comparison of the proposed procedure and parabolic model is presented graphically by examples.

Advanced thermoelastic heat conduction model with two ‎fractional parameters and phase-lags

2021 ◽  
Author(s):  
Ahmed E. Abouelregal ◽  
A. Soleiman‎ ◽  
Hamid M. Sedighi ◽  
K.M. Khalil‎ ◽  
M.E. Nasr‎
Keyword(s):  
Heat Conduction ◽  
Conduction Model ◽  
Heat Conduction Model ◽  
Phase Lags
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