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Nonlinear Vibrations and the Wave Equation

  • Book
  • © 2018

Overview

Authors:
  1. Alain Haraux

    1. National Center for Scientific Research, Université Pierre et Marie Curie, Paris, France

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  • Addresses the needs of PhD students
  • A self-contained resource
  • Provides an overview of the latest results in the field

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-x
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  2. Unbounded Linear Operators and Evolution Equations

    • Alain Haraux
    Pages 1-8

  3. A Class of Abstract Wave Equations

    • Alain Haraux
    Pages 9-14

  4. Almost Periodic Functions and the Abstract Wave Equation

    • Alain Haraux
    Pages 15-22

  5. The Wave Equation in a Bounded Domain

    • Alain Haraux
    Pages 23-26

  6. The Initial-Value Problem For A Mildly Perturbed Wave Equation

    • Alain Haraux
    Pages 27-33

  7. The Initial-Value Problem in Presence of a Strong Dissipation

    • Alain Haraux
    Pages 35-48

  8. Solutions on \(\mathbb {R}^{+}\) and Boundedness of the Energy

    • Alain Haraux
    Pages 49-54

  9. Existence of Forced Oscillations

    • Alain Haraux
    Pages 55-64

  10. Stability of Periodic or Almost Periodic Solutions

    • Alain Haraux
    Pages 65-71

  11. The Conservative Case in One Spatial Dimension

    • Alain Haraux
    Pages 73-82

  12. The Conservative Case in Several Spatial Dimensions

    • Alain Haraux
    Pages 83-90

  13. Recent Evolutions and Perspectives

    • Alain Haraux
    Pages 91-98

  14. Back Matter

    Pages 99-102
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Keywords

About this book

This book gathers the revised lecture notes from a seminar course offered at the Federal University of Rio de Janeiro in 1986, then in Tokyo in 1987. An additional chapter has been added to reflect more recent advances in the field.

Reviews

“The text is written in a lucid and reader-friendly style, and it requires only a basic knowledge of functional analysis to be understood. … This nice monograph is recommended to everybody interested in a concise but clear introduction to dissipative wave equations in bounded domains. It leads the reader to understand open problems in a classical research area which is still far from being completely explored.” (Enzo Vitillaro, Mathematical Reviews, December, 2018)

Authors and Affiliations

  • National Center for Scientific Research, Université Pierre et Marie Curie, Paris, France

    Alain Haraux

About the author

Prof. Alain Haraux studied at the Ecole Normale Superieure, Paris from 1969 to 1973. He became a researcher at the CNRS, France in 1973 and received his HDR (habilitation to conduct research) in Mathematics from the University of Paris 6 (now: Sorbonne University) in 1978. He is currently an Emeritus Director of Research at the CNRS, and is the author of more than 150 specialized papers and 6 books. Throughout his career, his main field of research has been the long-term behavior of the solutions to nonlinear partial differential equations, in particular such topics as stability, near-periodicity, oscillation theory, maximal attractors, stabilization theory and exact controllability.

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