Mathematical Models with Singularities

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.

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

Inhalt
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 conguration.- Radial oscillations of a bubble in a time-periodic pressure eld.- Radial oscillations of cylindrical and spherical shells.- A model for cell volume regulation.