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.
Publisher: Springer International Publishing AG
Number of pages: 444
Weight: 6922 g
Dimensions: 235 x 155 mm
Edition: 1st ed. 2018
"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)