 |
|
|
|
| HAL : hal-00648770, version 1 |
| DOI : 10.1016/j.na.2005.05.033 |
| Fiche détaillée |  Récupérer au format |
|
|
| Nonlinear Analysis: Theory, Methods and Applications Volume 63, Issue 8 (2005) Pages 1126-1152 |
|
|
|
|
| Nonlinear optimal control problems of degenerate parabolic equations with logistic time-varying delays of convolution type |
|
|
| Aziz Belmiloudi 1 |
|
|
| (31/12/2005) |
|
|
|
| In this article, we consider a bioeconomic model for optimal control problems which are governed by degenerate parabolic equations governing diffusive biological species with logistic growth terms and multiple time-varying delays. The time-varying delays are given in a convolution form. The existence, uniqueness and regularity results to the state equations with homogeneous Dirichlet and Neumann boundary conditions are established. The vanishing viscosity method is used to obtain the existence result. Afterwards, we formulate the optimal control problem in two cases. Firstly, we suppose that this biological species causes damage to environment (e.g. forest, agriculture): the optimal control is the trapping rate and the cost functional is a combination of damage and trapping costs. Secondly, an optimal harvesting control of a biological species is considered: the optimal control is a distribution of harvesting effort on the biological species and the cost functional measure the difference between economic revenue and cost. The existence and the condition of uniqueness of the optimal solution are obtained. A nonlinear optimality system is derived, characterizing the optimal control. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
|
|
|
CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
|
|
|
|
|
|
|
|
|
| Analyse numérique |
|
|
|
|
| Domaine | : | Mathématiques/Optimisation et contrôle Mathématiques/Equations aux dérivées partielles Mathématiques/Systèmes dynamiques |
|
|
| Optimal control – Degenerate parabolic equations – Logistic growth – Time-varying delays – Convolution type – Viscosity solution – Necessary conditions – Population dynamics |
|
| hal-00648770, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00648770 | |
| oai:hal.archives-ouvertes.fr:hal-00648770 | |
| Contributeur : Aziz Belmiloudi | |
| Soumis le : Mardi 6 Décembre 2011, 13:58:29 | |
| Dernière modification le : Vendredi 6 Janvier 2012, 14:56:35 | |
