Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Unstable simple modes of the nonlinear string

Authors: Thierry Cazenave and Fred B. Weissler
Journal: Quart. Appl. Math. 54 (1996), 287-305
MSC: Primary 35L70; Secondary 45G10, 73D35
DOI: https://doi.org/10.1090/qam/1388017
MathSciNet review: MR1388017
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Abstract: We prove instability of high-energy simple modes for the nonlinear vibrating string equation

$\displaystyle \left\{ {_{u\left\vert {_{\partial \Omega } = 0,} \right.}^{{u_{t... ...b \int_0^\pi {u_x^2 \left( {t, x} \right) dx} } \right) {u_{xx}} = 0,}} \right.$

in $ \Omega = \left( {0, \pi } \right)$, where $ a \ge 0, b > 0$.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/1388017
Article copyright: © Copyright 1996 American Mathematical Society

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