scholarly journals Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem

2007 ◽  
Vol 336 (2) ◽  
pp. 865-887 ◽  
Author(s):  
Assia Benabdallah ◽  
Yves Dermenjian ◽  
Jérôme Le Rousseau
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Discontinuous Coefficient ◽  
Carleman Estimates ◽  
One Dimensional ◽  
The One

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>

scholarly journals On the Reachable Set for the One-Dimensional Heat Equation

2018 ◽  
Vol 56 (3) ◽  
pp. 1692-1715 ◽  
Author(s):  
Jérémi Dardé ◽  
Sylvain Ervedoza
Keyword(s):  
Heat Equation ◽  
Reachable Set ◽  
One Dimensional ◽  
The One
Sign in / Sign up

Export Citation Format

Share Document