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Unstable simple modes of the nonlinear string

1996
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Quarterly of Applied Mathematics
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We prove instability of high-energy simple modes for the nonlinear vibrating string equation J utt -(a+ b /* ul(t, x) dx) uxx = 0, I u\dn = 0, in f] = (0,7r), where a > 0, b > 0. Resume. On montre l'instabilite des modes simples d'energie assez grande pour l'equation des cordes vibrantes non-lineaire utt -(a+ b ul(t, x) dx) uxx = 0, u\dn = 0, dans O = (0, ir), ou a > 0, b > 0. 1. Introduction. A classical model of the nonlinear vibrating string is given by the equation J utt -(a+ b fo ul(t,x)

doi:10.1090/qam/1388017
fatcat:2c2icgk7tjegdijaomrffczgom