Transport Equations in Biology

2007
ISBN: 978-3-7643-7841-7
Verlag: Springer

Buch, Englisch, 198 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 409 g

Reihe: Frontiers in Mathematics

This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. It develops appropriate mathematical tools and qualitative properties of the solutions (long time behavior, concentration phenomena, asymptotic behavior, regularizing effects, blow-up or dispersion). The book describes such original mathematical methods as the generalized relative entropy method, a unique method to tackle most of the problems in population biology; the description of Dirac concentration effects using a new type of Hamilton-Jacobi equations; and a general point of view on chemotaxis including various scales of description leading to kinetic, parabolic or hyperbolic equations.

Zielgruppe

Research

Autoren/Hrsg.

Perthame, Benoît

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Biowissenschaften Biowissenschaften Naturschutzbiologie, Biodiversität
• Naturwissenschaften Biowissenschaften Biowissenschaften Meeres- und Süßwasserökologie
• Naturwissenschaften Biowissenschaften Biowissenschaften Terrestrische Ökologie
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Biowissenschaften Biowissenschaften Ökologie

Inhaltsverzeichnis

From differential equations to structured population dynamics.- Adaptive dynamics; an asymptotic point of view.- Population balance equations: the renewal equation.- Population balance equations: size structure.- Cell motion and chemotaxis.- General mathematical tools.