RESOLUTION AND NUMERICAL SIMULATION OF A CONTROL PROBLEM OF THE HEAT EQUATION
Keywords:
heat equation, existence of the solution, uniqueness of the solution, coupling of the Adomian decompositional method and the spectral methodDOI:
https://doi.org/10.17654/0975045223001Abstract
We present the resolution and numerical simulation of an optimal control problem of the heat equation. We have proved the existence and uniqueness of the solution of the equation of state. Then we obtain the approximation of the optimization problem and a numerical solution of the model problem based on coupling of the Adomian decompositional method and the spectral method. Numerical simulations of the model have also been presented and error estimates for some parameter values have been given.
Received: September 6, 2022
Accepted: September 28, 2022
References
A. S. Ackleh and B. G. Fitzpatrick, Approximation and parameter estimation problems for Algal Aggregations models, Maths. Models. Methods in Appl. Science 4(3) (1994), 291-311.
Balira Ousmane Konfe, Nouvelles méthodes mathématiques Alienor et Adpmian, pour la biomedécine, Université de Ouagadougou, Thèse, 2005.
B. Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge University Press, Cambridge, UK, 1996.
Bisso Saley, Résolution et simulation numérique d’un problème de contrôle optimale gouverné par des équations aux dérivées partielles de type diffusion-réaction issues de la modélisation mathématique en traitement du cancer du cerveau, Université de Ouagadougou, Thèse, 2003.
Bisso Saley and Benjamin Mampassi, Solving large scale PDE optimisation problems with a decomposition scheme, Pioneer Scientific Publisher, (2011), 127-146.
D. Gottlieb and J. S. Hesthaven, Spectral methods for hyperbolic problems, Journal of Computational and Applied Mathematics 128 (2001), 83-131.
Haïm Brezis, Analyse fonctionnelle, théorie et applications, Masson, 1987.
H. T. Banks, On a variational approach to some parameter estimation problems, distributed parameter systems (Vorau, 1984) Lecture Notes in Control Inf. Sci., Vol. 75, Springer, Berlin, 1985, pp. 1-23.
Djibo Moustapha and Saley Bisso, Resolution and numerical simulation of an optimal control problem of surface water pollution, International Journal of Differential Equations and Applications 17(1) (2018), 1-31. http://www.ijpam.eu
Jacques Lious Lions, Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles, Dunod, Paris, 1968.
Maintine Bergounioux, Optimisation et contrôle des systèmes linéaire, Dunod, Paris, 2001.
O. Thual, Introduction aux méthodes spectrales, Institut National Polytechnique de Toulouse, 1996.
Y. Cherruault, Sur la convergence de la méthode d’Adomian, RAIRO, Recherche Opérationnelle, tome 22(3) (1988), 291-299.
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