Asymptotics of Elliptic and Parabolic PDEs

Asymptotics of Elliptic and Parabolic PDEs

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

Holcman, David; Schuss, Zeev

Springer International Publishing AG

06/2018

444

Dura

Inglês

9783319768946

15 a 20 dias

6922

Descrição não disponível.
Part I. Singular Perturbations of Elliptic Boundary Problems.- 1 Second-Order Elliptic Boundary Value Problems with a Small Leading Part.- 2 A Primer of Asymptotics for ODEs.- 3 Singular Perturbations in Higher Dimensions.- 4 Eigenvalues of a Non-self-adjoint Elliptic Operator.- 5 Short-time Asymptotics of the Heat Kernel.- Part II Mixed Boundary Conditions for Elliptic and Parabolic Equations.- 6 The Mixed Boundary Value Problem.- 7 THe Mixed Boundary Value Problem in R2.- 8 Narrow Escape in R3.- 9 Short-time Asymptotics of the Heat Kernel and Extreme Statistics of the NET.- 10 The Poisson-Nernst-Planck Equations in a Ball.- 11 Reconstruction of Surface Diffusion from Projected Data.- 12 Asymptotic Formulas in Molecular and Cellular Biology.- Bibliography.- Index.
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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