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＜E-Book＞
Parabolic Equations in Biology : Growth, reaction, movement and diffusion / by Benoît Perthame
(Lecture Notes on Mathematical Modelling in the Life Sciences. ISSN:21934797)

Edition	1st ed. 2015.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2015
Language	English
Size	XII, 199 p. 39 illus., 13 illus. in color : online resource
Authors	*Perthame, Benoît author SpringerLink (Online service)
Subjects	LCSH:Biomathematics LCSH:Mathematics FREE:Mathematical and Computational Biology FREE:Applications of Mathematics
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-319-19500-1

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