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Introduction

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1522)

Abstract

We will first recall some elementary results concerning the Cauchy problem for the linear wave equation. Then, we will indicate the new phenomenons appearing in the study of semilinear wave equations and we will describe the theorems obtained by Beals, Bony, Melrose-Ritter about semilinear Cauchy problems with conormal data. Lastly, we will state “swallow-tail’s problem”, which will be solved in the last chapter of this text, where we expose a method due to Lebeau.

Keywords

  • Cauchy Problem
  • Light Cone
  • Pinching Point
  • Linear Wave Equation
  • Sobolev Regularity

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1992 Springer-Verlag Berlin Heidelberg

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Delort, JM. (1992). Introduction. In: F.B.I. Transformation. Lecture Notes in Mathematics, vol 1522. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21539-5_1

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  • DOI: https://doi.org/10.1007/978-3-662-21539-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55764-7

  • Online ISBN: 978-3-662-21539-5

  • eBook Packages: Springer Book Archive