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


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.


Weak Solution Saddle Point Euler Equation Finite Time Nonlinear Wave Equation 
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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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