TY  - BOOK
AU  - Perthame,Benoît
ED  - SpringerLink (Online service)
TI  - Parabolic Equations in Biology: Growth, reaction, movement and diffusion 
T2  - Lecture Notes on Mathematical Modelling in the Life Sciences,
SN  - 9783319195001
AV  - QH323.5 
U1  - 570.285 23
PY  - 2015///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - mathematics
KW  - Applied mathematics
KW  - Engineering mathematics
KW  - Biomathematics
KW  - Mathematics
KW  - Mathematical and Computational Biology
KW  - Applications of Mathematics
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-319-19500-1
ER  -