Parabolic Equations in Biology: Growth, reaction, movement and diffusion: Lecture Notes on Mathematical Modelling in the Life Sciences
Autor Benoît Perthameen Limba Engleză Paperback – 17 sep 2015
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Specificații
ISBN-13: 9783319194998
ISBN-10: 3319194992
Pagini: 199
Ilustrații: XII, 199 p. 39 illus., 13 illus. in color.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 3.29 kg
Ediția:1st ed. 2015
Editura: Springer International Publishing
Colecția Springer
Seria Lecture Notes on Mathematical Modelling in the Life Sciences
Locul publicării:Cham, Switzerland
ISBN-10: 3319194992
Pagini: 199
Ilustrații: XII, 199 p. 39 illus., 13 illus. in color.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 3.29 kg
Ediția:1st ed. 2015
Editura: Springer International Publishing
Colecția Springer
Seria Lecture Notes on Mathematical Modelling in the Life Sciences
Locul publicării:Cham, Switzerland
Public țintă
GraduateCuprins
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.
Recenzii
“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)
Notă biografică
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.
Textul de pe ultima copertă
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.
Caracteristici
Provides the basic content for a course at master level on fundamental models in mathematics used for modeling in biology 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