Asymptotics of Elliptic and Parabolic PDEs and their Applications in Statistical Physics, Computational Neuroscience, and Biophysics

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Synopsis

This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences.

In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory.

Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.

Book details

Edition:
1st ed. 2018
Series:
Applied Mathematical Sciences (Book 199)
Author:
David Holcman, Zeev Schuss
ISBN:
9783319768953
Related ISBNs:
9783319768946
Publisher:
Springer International Publishing
Pages:
N/A
Reading age:
Not specified
Includes images:
Yes
Date of addition:
2018-10-18
Usage restrictions:
Copyright
Copyright date:
2018
Copyright by:
Springer International Publishing AG 
Adult content:
No
Language:
English
Categories:
Earth Sciences, Mathematics and Statistics, Nonfiction, Science