Israel Journal of Mathematics

, Volume 22, Issue 3–4, pp 273–303 | Cite as

Saddle points and instability of nonlinear hyperbolic equations

  • L. E. Payne
  • D. H. Sattinger
Article

Abstract

A number of authors have investigated conditions under which weak solutions of the initial-boundary value problem for the nonlinear wave equation will blow up in a finite time. For certain classes of nonlinearities sharp results are derived in this paper. Extensions to parabolic and to abstract operator equations are also given.

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Copyright information

© Hebrew University 1976

Authors and Affiliations

  • L. E. Payne
    • 1
    • 2
  • D. H. Sattinger
    • 1
    • 2
  1. 1.Cornell UniversityUSA
  2. 2.University of MinnesotaUSA

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