On the Korteweg-de Vries equation View Full Text


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Article Info

DATE

1979-01

AUTHORS

Tosio Kato

ABSTRACT

Existence, uniqueness, and continuous dependence on the initial data are proved for the local (in time) solution of the (generalized) Korteweg-de Vries equation on the real line, with the initial function ϕ in the Sobolev space of order s>3/2 and the solution u(t) staying in the same space, s=∞ being included For the proper KdV equation, existence of global solutions follows if s≥2. The proof is based on the theory of abstract quasilinear evolution equations developed elsewhere. More... »

PAGES

89-99

References to SciGraph publications

  • 1976-03. Remarks on the Korteweg-de Vries equation in ISRAEL JOURNAL OF MATHEMATICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01647967

    DOI

    http://dx.doi.org/10.1007/bf01647967

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1039529393


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