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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 field.- Bose-Einstein condensates and signal transmission in optical fibers.- Electron beam focusing by means of a periodic magnetic field.- Point vortex dynamics.- Pumping effect in a pipe/tank flow configuration.- Radial oscillations of a bubble in a time-periodic pressure field.- Radial oscillations of cylindrical and spherical shells.- A model for cell volume regulation.
Description
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.
