Asymptotics of Elliptic and Parabolic PDEs - pr_35833

Asymptotics of Elliptic and Parabolic PDEs

and their Applications in Statistical Physics, Computational Neuroscience, and Biophysics

By David Holcman, Zeev Schuss



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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.

Product code: 9783319768946

ISBN 9783319768946
Publisher Springer International Publishing AG
No. Of Pages 444
Dimensions (HxWxD in mm) H235xW155
Edition 1st ed. 2018
Series Applied Mathematical Sciences