Mathematical Models with Singularities [electronic resource] : A Zoo of Singular Creatures /
Torres, Pedro J.author.
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.
Description based upon print version of record.
Includes bibliographical references and index.
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.
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.
Differential equations.
Mathematical physics.
Ordinary Differential Equations.
Mathematical Applications in the Physical Sciences.