Open AccessIdentifying the heat sink
Author(s) -
Johnson D. Audu,
Amin Boumenir,
K. M. Furati,
I. O. Sarumi
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021164
Subject(s) - heat equation , heat sink , boundary value problem , sink (geography) , inverse , inverse problem , mathematics , matrix (chemical analysis) , computer science , mathematical analysis , physics , thermodynamics , materials science , geometry , geography , cartography , composite material
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.