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Parabolic Equations in Biology

Growth, reaction, movement and diffusion

Benoît Perthame (Autor)

Buch | Softcover

XII, 199 Seiten

2015 | 1st ed. 2015
Springer International Publishing (Verlag)
978-3-319-19499-8 (ISBN)

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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.

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.

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 a variety of phenomena arising in the analysis of partial differential equations modelling of biological, physical and chemical processes. ... This book can well serve as a textbook for a course on master's level. Exercise problems are given in each chapter." (Jonathan Zinsl, zbMATH 1333.35001, 2016)

Erscheint lt. Verlag	17.9.2015
Reihe/Serie	Lecture Notes on Mathematical Modelling in the Life Sciences
Zusatzinfo	XII, 199 p. 39 illus., 13 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Informatik ► Weitere Themen ► Bioinformatik
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Fokker-Planck Equations • Mathematical Biology • Reaction-diffusion • traveling waves • Turing patterns
ISBN-10	3-319-19499-2 / 3319194992
ISBN-13	978-3-319-19499-8 / 9783319194998
Zustand	Neuware