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Mathematical Models with Singularities

A Zoo of Singular Creatures

  • Book
  • © 2015

Overview

Authors:
  1. Pedro J. Torres

    1. Department of Applied Mathematics, University of Granada, Granada, Spain

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  • 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

Part of the book series: Atlantis Briefs in Differential Equations (ABDE, volume 1)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Motion of Charged Particles in a Line

    • Pedro J. Torres
    Pages 1-14

  3. An Electrostatically Actuated Micro-electro-mechanical System

    • Pedro J. Torres
    Pages 15-20

  4. Forced Keplerian-Like Systems

    • Pedro J. Torres
    Pages 21-27

  5. Particles Under a Central Force Field

    • Pedro J. Torres
    Pages 29-41

  6. Bose-Einstein Condensates and Signal Transmission in Optical Fibers

    • Pedro J. Torres
    Pages 43-58

  7. Electron Beam Focusing by Means of a Periodic Magnetic Field

    • Pedro J. Torres
    Pages 59-68

  8. Point Vortex Dynamics

    • Pedro J. Torres
    Pages 69-83

  9. Pumping Effect in a Pipe/Tank Flow Configuration

    • Pedro J. Torres
    Pages 85-91

  10. Radial Oscillations of a Bubble in a Time-Periodic Pressure Field

    • Pedro J. Torres
    Pages 93-98

  11. Radial Oscillations of Cylindrical and Spherical Shells

    • Pedro J. Torres
    Pages 99-105

  12. A Model for Cell Volume Regulation

    • Pedro J. Torres
    Pages 107-112

  13. Back Matter

    Pages 113-124
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Applied Mathematics, University of Granada, Granada, Spain

    Pedro J. Torres

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