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.
Series
Edition
Language
Place of publication
Publishing group
Target group
Professional and scholarly
Research
Illustrations
28 s/w Abbildungen
VIII, 198 p. 28 illus.
Dimensions
Height: 254 mm
Width: 178 mm
Thickness: 12 mm
Weight
ISBN-13
978-3-7643-7841-7 (9783764378417)
DOI
10.1007/978-3-7643-7842-4
Schweitzer Classification
Benoit Perthame is presently a Professor at the University Pierre et Marie Curie where he heads the Laboratoire Jacques-Louis Lions. Before that he was a professor at Ecole Normale Supérieure in Paris where he begun to develop a research ideated to several aspects of mathematical biology: collective motion of cells, adaptation and evolution theory, modeling in tumor growth and therapy. Benoit Perthame was a plenary speaker at ICM Seoul, 2014.
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.
