Overview
- Discusses asymptotic formulae in the context of the life sciences
- Presents applications in molecular and cellular biology, biophysics, as well as computational neuroscience
- Contains over 100 figures
- Includes bibliographical notes
Part of the book series: Applied Mathematical Sciences (AMS, volume 199)
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Table of contents (12 chapters)
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Front Matter
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Singular Perturbations of Elliptic Boundary Problems
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Front Matter
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Mixed Boundary Conditions for Elliptic and Parabolic Equations
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Front Matter
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Back Matter
Keywords
- boundary value problems
- Poisson-Nernst-Planck
- extreme statistics
- narrow escape
- first passage times
- asymptotic formula
- partial differential equations
- WKB
- eigenvalues
- matched asymptotics
- non-self adjoint operators
- short-time asymptotics
- long-time asymptotics
- Green’s functions
- Neumann’s function
- applied conformal transformation
- Eikonal equation
- Ray method
- Helmholtz equation
- integral equations
About this book
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 inderiving solutions to real-world problems from first principles.Reviews
“The monograph under review deals with asymptotic methods for the construction of solutions to boundary value problems for partial differential equations arising in applications, as molecular and cellular biology and biophysics. … The monograph is well written, interesting, and surely recommended to applied mathematicians, engineers, physicists, chemists, and neuroscientists interested into analytical methods for the asymptotic analysis of elliptic and parabolic PDEs of relevance in applications.” (Paolo Musolino, zbMATH 1402.35004, 2019)
Authors and Affiliations
About the authors
Zeev Schuss is an applied mathematician who significantly shaped the field of modern asymptotics in PDEs with applications to first passage time problems. Methods developed have been applied to various fields, including signal processing, statistical physics, and molecular biophysics.
Bibliographic Information
Book Title: Asymptotics of Elliptic and Parabolic PDEs
Book Subtitle: and their Applications in Statistical Physics, Computational Neuroscience, and Biophysics
Authors: David Holcman, Zeev Schuss
Series Title: Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-3-319-76895-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-76894-6Published: 06 June 2018
Softcover ISBN: 978-3-030-08319-9Published: 05 January 2019
eBook ISBN: 978-3-319-76895-3Published: 25 May 2018
Series ISSN: 0066-5452
Series E-ISSN: 2196-968X
Edition Number: 1
Number of Pages: XXIII, 444
Number of Illustrations: 47 b/w illustrations, 56 illustrations in colour
Topics: Partial Differential Equations, Mathematical Applications in the Physical Sciences, Numerical and Computational Physics, Simulation, Mathematical and Computational Biology, Mathematical Methods in Physics, Biological and Medical Physics, Biophysics