| Publication type: |
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Conference, seminar, workshop communication |
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| Subject: |
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| Title: |
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Optimal control problems of nonlinear parabolic systems with logistic time-varying delays |
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| Author(s): |
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Aziz Belmiloudi ( ) 1 |
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| Laboratory: |
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| Research team: |
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Analyse numérique |
| Abstract: |
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In this contribution, we study a bioeconomic model for optimal control problems for a class of systems governed by parabolic equations governing diffusive biological species with logistic growth terms and time-varying delays. Indeed, we must take account of the influence of the population at earlier times and the time to reach maturity, the finished period of gestation, etc, because the birth rate does not act instantaneously. The pronostic function u(x; t) is the biological species concentration. It is dependent on the rate of trapping the species, the spacially dependent intrinsic growth, the crowding effect and the time-varying delays. We prove the existence, uniqueness and regularity results to the states equations with homogeneous Dirichlet and Neumann boundary conditions. The existence result is based on the construction of a monotone decreasing sequence of solutions convergent towards the solution. Afterwards, we formulate the optimal control problem. We suppose that this biological species causes damage to environment (forest, farming, etc): the optimal control is the trapping rate and the cost functional is a combination of damage and trapping costs. The existence and the condition of uniqueness of the optimal solution are derived. First order necessary conditions of optimality are obtained. The optimality system is corresponding to identify the gradient of the cost function that is necessary to develop a numerical scheme in order to solve the optimal control problem. |
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| Fulltext language: |
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English |
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| Audience: |
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international |
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| Conference or book title: |
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Workshop on shape optimization in life sciences and environment |
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| Conference date: |
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2004-03-25 |
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| Conference date (end): |
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2004-03-26 |
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| City: |
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Toulouse |
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| Country: |
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France |
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| Keyword(s): |
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bioeconomic model – Optimal control – logistic growth – time-varying delays |
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