Transport Equations in Biology

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. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions. The book further contains many original PDE problems originating in biosciences.

Sommario

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.

Riassunto

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.

Dettagli sul prodotto

• Autori: Benoit Perthame, Benoît Perthame
• Editore: Birkhäuser
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 01.01.2006
• EAN: 9783764378417
• ISBN: 978-3-7643-7841-7
• Pagine: 208
• Peso: 415 g
• Serie: Frontiers in Mathematics; Frontiers in Mathematics
• Categorie: Scienze naturali, medicina, informatica, tecnica > Biologia > Ecologia; Analysis, B, DV-gestützte Biologie/Bioinformatik, Kybernetik und Systemtheorie, Differentialrechnung und -gleichungen, Ecology, Dynamics, Mathematics and Statistics, Ordinary Differential Equations, Dynamical Systems and Ergodic Theory, Ergodic theory, Nonlinear science, Differential calculus & equations, Differential equations, Dynamical systems, Maths for scientists, Biomathematics, Mathematical and Computational Biology