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Asymptotics of elliptic and parabolic PDEs : and their Applications in Statistical Physics, Computational Neuroscience, and Biophysics / by David Holcman, Zeev Schuss.

9783319768953 (electronic book)
3319768956 (electronic book)
9783319768946
3319768948

Cham, Switzerland : Springer, 2018.

English

1 online resource (xxiii, 444 pages) : illustrations.

10.1007/978-3-319-76895-3 doi

QA377

515/.3533

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.

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Online resource; title from PDF title page (SpringerLink, viewed May 31, 2018).

Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 199.

Print version: 9783319768946

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