Asymptotics of Elliptic and Parabolic PDEs: and their Applications in Statistical Physics, Computational Neuroscience, and Biophysics - Softcover

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.