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Autor: Benoît Perthame
ISBN-13: 9783319194998
Einband: Taschenbuch
Seiten: 199
Gewicht: 349 g
Format: 236x155x12 mm
Sprache: Englisch

Parabolic Equations in Biology

Lecture Notes on Mathematical Modelling in the Life Sciences
Growth, reaction, movement and diffusion
1.Parabolic Equations in Biology.- 2.Relaxation, Perturbation and Entropy Methods.- 3.Weak Solutions of Parabolic Equations in whole Space.- 4.Traveling Waves.- 5.Spikes, Spots and Pulses.- 6.Blow-up and Extinction of Solutions.- 7.Linear Instability, Turing Instability and Pattern Formation.- 8.The Fokker-Planck Equation.- 9.From Jumps and Scattering to the Fokker-Planck Equation.- 10.Fast Reactions and the Stefan free Boundary Problem.
This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.
Autor: Benoît Perthame
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.
Autor: Benoît Perthame
ISBN-13:: 9783319194998
ISBN: 3319194992
Verlag: Springer, Berlin, Springer International Publishing
Gewicht: 349g
Seiten: 199
Sprache: Englisch
Auflage 1st ed.
Sonstiges: Taschenbuch, 236x155x12 mm, 26 SW-Abb., 13 Farbabb.