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New Methods and Results in Non-linear Field Equations

Proceedings of a Conference Held at the University of Bielefeld, Federal Republic of Germany, 7–10 July 1987

  • Conference proceedings
  • © 1989

Overview

Editors:
  1. Philippe Blanchard
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  2. Joao-Paulo Dias
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  3. Joachim Stubbe
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Part of the book series: Lecture Notes in Physics (LNP, volume 347)

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Table of contents (9 papers)

  1. Front Matter

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  2. Some remarks on stochastically perturbed (Hamiltonian) systems

    • Sergio Albeverio, Astrid Hilbert
    Pages 1-18

  3. Stability of ground states for nonlinear classical field theories

    • Ph. Blanchard, J. Stubbe
    Pages 19-35

  4. A note on solutions of two-dimensional semilinear elliptic vector-field equations with strong nonlinearity

    • E. Brüning
    Pages 37-57

  5. Some remarks on the nonlinear Schrödinger equation in the subcritical case

    • Thierry Cazenave, Fred B. Weissler
    Pages 59-69

  6. The Cauchy problem for the Dirac equation with cubic nonlinearity in three space dimensions

    • João-Paulo Dias, Mário Figueira
    Pages 71-78

  7. The Cauchy problem for the non-linear Klein-Cordon equation

    • J. Ginibre, G. Velo
    Pages 79-90

  8. Conformal invariance and time decay for nonlinear wave equations

    • J. Ginibre, G. Velo
    Pages 91-113

  9. Energy forms and white noise analysis

    • T. Hida, J. Potthoff, L. Streit
    Pages 115-125

  10. Principles of solitary wave stability

    • Luis Vazquez
    Pages 127-133

  11. Back Matter

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Keywords

About this book

Quantum effects may be modelled by means of stochastic perturbation of non-linear partial differential (field) equations. Contributions to this field of research are collected in this volume. Finite dimensional stochastically perturbed Hamiltonian systems and infinite dimensional white noise analysis are treated. The main part concerns problems encountered in deterministic equations. Papers treat the existence of solutions for given initial data, the existence of non-linear bound states or solitary waves including a thorough discussion of various approaches to stability, and global properties (e.g. time decay properties) for non-linear wave equations. This volume provides a good survey of present-day research in non-linear problems of quantum theory for researchers and graduate students.

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