Ebook: Analysis and Control of Age-Dependent Population Dynamics

The material of the present book is an extension of a graduate course given by the author at the University "Al.I. Cuza" Iasi and is intended for stu­ dents and researchers interested in the applications of optimal control and in mathematical biology. Age is one of the most important parameters in the evolution of a bi­ ological population. Even if for a very long period age structure has been considered only in demography, nowadays it is fundamental in epidemiology and ecology too. This is the first book devoted to the control of continuous age structured populationdynamics.It focuses on the basic properties ofthe solutions and on the control of age structured population dynamics with or without diffusion. The main goal of this work is to familiarize the reader with the most important problems, approaches and results in the mathematical theory of age-dependent models. Special attention is given to optimal harvesting and to exact controllability problems, which are very important from the econom­ ical or ecological points of view. We use some new concepts and techniques in modern control theory such as Clarke's generalized gradient, Ekeland's variational principle, and Carleman estimates. The methods and techniques we use can be applied to other control problems.

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This volume is devoted to some of the most biologically significant control problems governed by continuous age-dependent population dynamics. It investigates the existence, uniqueness, positivity, and asymptotic behaviour of the solutions of the continuous age-structured models. Some comparison results are also established. In the optimal control problems the emphasis is on first order necessary conditions of optimality. These conditions allow the determination of the optimal control or the approximation of the optimal control problem. The exact controllability for some models with diffusion and internal control is also studied. These subjects are treated using new concepts and techniques of modern optimal control theory, such as Clarke's generalized gradient, Ekeland's variational principle, Hamilton-Jacobi equations, and Carleman estimates. A background in advanced calculus and partial differential equations is required.
Audience: This work will be of interest to students in mathematics, biology, and engineering, and researchers in applied mathematics, control theory, and biology.

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This volume is devoted to some of the most biologically significant control problems governed by continuous age-dependent population dynamics. It investigates the existence, uniqueness, positivity, and asymptotic behaviour of the solutions of the continuous age-structured models. Some comparison results are also established. In the optimal control problems the emphasis is on first order necessary conditions of optimality. These conditions allow the determination of the optimal control or the approximation of the optimal control problem. The exact controllability for some models with diffusion and internal control is also studied. These subjects are treated using new concepts and techniques of modern optimal control theory, such as Clarke's generalized gradient, Ekeland's variational principle, Hamilton-Jacobi equations, and Carleman estimates. A background in advanced calculus and partial differential equations is required.
Audience: This work will be of interest to students in mathematics, biology, and engineering, and researchers in applied mathematics, control theory, and biology.
Content:
Front Matter....Pages i-ix
Introduction....Pages 1-14
Analysis of Age-Dependent Population Dynamics....Pages 15-64
Optimal Control of Population Dynamics....Pages 65-108
Analysis of Population Dynamics with Diffusion....Pages 109-136
Control of Population Dynamics with Diffusion....Pages 137-170
Back Matter....Pages 171-201

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This volume is devoted to some of the most biologically significant control problems governed by continuous age-dependent population dynamics. It investigates the existence, uniqueness, positivity, and asymptotic behaviour of the solutions of the continuous age-structured models. Some comparison results are also established. In the optimal control problems the emphasis is on first order necessary conditions of optimality. These conditions allow the determination of the optimal control or the approximation of the optimal control problem. The exact controllability for some models with diffusion and internal control is also studied. These subjects are treated using new concepts and techniques of modern optimal control theory, such as Clarke's generalized gradient, Ekeland's variational principle, Hamilton-Jacobi equations, and Carleman estimates. A background in advanced calculus and partial differential equations is required.
Audience: This work will be of interest to students in mathematics, biology, and engineering, and researchers in applied mathematics, control theory, and biology.
Content:
Front Matter....Pages i-ix
Introduction....Pages 1-14
Analysis of Age-Dependent Population Dynamics....Pages 15-64
Optimal Control of Population Dynamics....Pages 65-108
Analysis of Population Dynamics with Diffusion....Pages 109-136
Control of Population Dynamics with Diffusion....Pages 137-170
Back Matter....Pages 171-201
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