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Parabolic equations in biology. Growth, reaction, movement and diffusion. (English) Zbl 1333.35001
Lecture Notes on Mathematical Modelling in the Life Sciences. Cham: Springer (ISBN 978-3-319-19499-8/pbk; 978-3-319-19500-1/ebook). xii, 199 p. (2015).
This book presents a variety of phenomena arising in the analysis of partial differential equations modelling of biological, physical and chemical processes. Specifically (and in contrast to the author’s book [Transport equations in biology. Frontiers in Mathematics. Basel: Birkhäuser (2007; Zbl 1185.92006)]), it is focussed on (in many cases nonlinear) parabolic equations and phenomena related to pattern formation such as Turing instability or travelling waves. In addition, this book gives a concise introduction to more fundamental topics in the theory of partial differential equations, for example, notions of weak solutions or blow-up of solutions. The specific modelling aspects of each set of equations are presented in detail; furthermore, the mathematical results are put into connection with their biological background and in most cases illustrated by simulations. This book can well serve as a textbook for a course on master’s level. Exercise problems are given in each chapter.

MSC:
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35B36 Pattern formations in context of PDEs
35Q84 Fokker-Planck equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92B05 General biology and biomathematics
35K57 Reaction-diffusion equations
35B44 Blow-up in context of PDEs
35C07 Traveling wave solutions
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