Analysis and Control of Age-Dependent Population Dynamics

1. Auflage. Softcover version of original hardcover Auflage 2000
ISBN: 978-90-481-5590-3
Verlag: Springer Netherlands

Buch, Englisch, Band 11, 201 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 330 g

Reihe: Mathematical Modelling: Theory and Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Anita, S.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Sozialwissenschaften Soziologie | Soziale Arbeit Soziologie Allgemein Demographie, Demoskopie
• Naturwissenschaften Biowissenschaften Biowissenschaften
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis

Inhaltsverzeichnis

1 Introduction.- 2 Analysis of Age-Dependent Population Dynamics.- 3 Optimal Control of Population Dynamics.- 4 Analysis of Population Dynamics with Diffusion.- 5 Control of Population Dynamics with Diffusion.- Appendix 1: Elements of Nonlinear Analysis.- A1.1 Convex functions and subdifferentials.- A1.2 Generalized gradients of locally Lipschitz functions.- A1.3 The Ekeland variational principle.- Appendix 2: The Linear Heat Equation.- References.