Asymptotics of Elliptic and Parabolic PDEs
and their Applications in Statistical Physics, Computational Neuroscience, and Biophysics
Buch in deiner Nähe kaufen
Beschreibung
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.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 inderiving solutions to real-world problems from first principles.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
Autor*in
David Holcman
Themen in »Asymptotics of Elliptic and Parabolic PDEs«
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
Stimmen zu »Asymptotics of Elliptic and Parabolic PDEs«
“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)
()