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Article . 1993 . Peer-reviewed
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Focusing and absorption of nonlinear oscillations

Authors: Joly, J. L.; Métivier, G.; Rauch, J.;

Focusing and absorption of nonlinear oscillations

Abstract

The Cauchy problem for the dissipative wave equation \[ u_{tt} - \Delta u + u | u |^ p = 0, \quad t > 0, \quad x \in \mathbb{R}^ d \] with fast oscillating initial functions is considered. The problem is a passage of the fast oscillating wave through a focal point, where the wave amplitude is increasing that is predicted by the geometric optics method. The main result is as follows: The oscillations which may be present in the initial data do not survive a passage through the focus, if \((d-1)p \geq 2\).

Keywords

fast oscillating initial functions, Geometric optics, Second-order nonlinear hyperbolic equations, passage of the fast oscillating wave through a focal point

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
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