Mathematical Models with Singularities: A Zoo of Singular Creatures [Paperback]

The book aims to provide an unifying view of a variety (a 'zoo') of mathematical models with some kind of singular nonlinearity, in the sense that it becomes infinite when the state variable approaches a certain point. Up to 11 different concrete models are analyzed in separate chapters. Each chapter starts with a discussion of the basic model and its physical significance. Then the main results and typical proofs are outlined, followed by open problems. Each chapter is closed by a suitable list of references. The book may serve as a guide for researchers interested in the modelling of real world processes.Motion of charged particles in a line.- An electrostatically actuated micro-electro-mechanical system.- Forced Keplerian-like systems.- Particles under a central force
eld.- Bose-Einstein condensates and signal transmission in optical
bers.- Electron beam focusing by means of a periodic magnetic
eld.- Point vortex dynamics.- Pumping effect in a pipe/tank ow con
guration.- Radial oscillations of a bubble in a time-periodic pressure
eld.- Radial oscillations of cylindrical and spherical shells.- A model for cell volume regulation.A collection of models with singularities is presented Each chapter presents the history of the model and the current state of the art Interesting open problems are pointed out as a guide for future research Includes supplementary material: sn.pub/extras