| Dewey Class |
570.285 |
| Title |
Parabolic Equations in Biology ([EBook]) : Growth, reaction, movement and diffusion / / by Benoît Perthame. |
| Author |
Perthame, Benoît |
| Other name(s) |
SpringerLink (Online service) |
| Publication |
Cham : : Springer International Publishing : : Imprint: Springer, , 2015. |
| Physical Details |
XII, 199 p. 39 illus., 13 illus. in color. : online resource. |
| Series |
Lecture Notes on Mathematical Modelling in the Life Sciences 2193-4789 |
| ISBN |
9783319195001 |
| Summary Note |
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.: |
| Contents note |
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. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
http://dx.doi.org/10.1007/978-3-319-19500-1 |
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