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Saddle points and instability of nonlinear hyperbolic equations

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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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The publication of this research is supported in part by NSF Grant 21806 (DHS) and by NSF Grant GP33031X (LEP).

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Payne, L.E., Sattinger, D.H. Saddle points and instability of nonlinear hyperbolic equations. Israel J. Math. 22, 273–303 (1975). https://doi.org/10.1007/BF02761595

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  • DOI: https://doi.org/10.1007/BF02761595

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