Saddle points and instability of nonlinear hyperbolic equations
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.
KeywordsWeak Solution Saddle Point Euler Equation Finite Time Nonlinear Wave Equation
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- 2.K. Jörgens,Nonlinear wave equations, Lecture Notes, University of Colorado, March, 1970.Google Scholar
- 11.D. H. Sattinger,Topics in Stability and Bifurcation Theory, Springer Lecture Notes in Mathematics, 309.Google Scholar
- 12.J. Serrin,Nonlinear Elliptic Equations of Second Order, AMS Symposium in Partial Differential Equations, Berkeley, Calif., August, 1971.Google Scholar