Parabolic Equations in Biology - Growth, reaction, movement and diffusion
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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.
Includes applications to ecology and population dynamics, neurosciences, enzymatic reactions and chemotaxis
Presents an original and rigorous presentation of several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations
"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)