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Semilinear geometric optics with boundary amplification

2014
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Analysis & PDE
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We study weakly stable semilinear hyperbolic boundary value problems with highly oscillatory data. Here weak stability means that exponentially growing modes are absent, but the so-called uniform Lopatinskii condition fails at some boundary frequency $\beta$ in the hyperbolic region. As a consequence of this degeneracy there is an amplification phenomenon: outgoing waves of amplitude $O(\eps^2)$ and wavelength $\eps$ give rise to reflected waves of amplitude $O(\eps)$, so the overall solution

doi:10.2140/apde.2014.7.551
fatcat:7lktdtuyzfazxcflfvuaea3itm