Abstract
The purpose of these first two lectures is to describe several unsolved problems in the general theory of non-linear wave equations. By “general”, I mean techniques which are not too sensitive to the form of the equation. So I will not discuss the inverse scattering method or the recent work on the Korteweg-de Vries or Sine-Gordon equations which exploits the special properties of those equations. Today I will lecture on the local and global existence theory and tomorrow on the scattering theory. A note of warning is in order perhaps. The problems have varying degrees of difficulty. Some of them are difficult indeed and have resisted the efforts of many analysts. Others are reasonably straightforward problems on which it should be easy to make substantial and interesting progress. Still others are so vaguely stated that they could be easy or hard depending on how they are interpreted.
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© 1978 Plenum Press, New York
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Reed, M. (1978). Unsolved Problems in the Theory of Non-Linear Wave Equations. In: Streit, L. (eds) Many Degrees of Freedom in Field Theory. NATO Advanced Study Institutes Series, vol 30. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8924-2_5
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