Geometric optics expansions for hyperbolic corner problems II : from weak stability to violent instability

Antoine Benoit 1, 2, *
* Corresponding author
1 MEPHYSTO - Quantitative methods for stochastic models in physics
LPP - Laboratoire Paul Painlevé - UMR 8524, ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe
Abstract : In this article we are interested in the rigorous construction of geometric optics expansions for weakly well-posed hyperbolic corner problems. More precisely we focus on the case where selfinteracting phases occur and are exactly the phases where the uniform Kreiss-Lopatinskii condition fails. We then show that the associated WKB expansion suffers arbitrarily many amplifications in a fixed finite time. As a consequence, we show that this corner problem can not be well-posed even at the price of a huge loss of derivatives. The new result, in that framework, is that the violent instability does not come from the failure of the weak Kreiss-Lopatinskii condition, but of the accumulation of arbitrarily many weak instabilities.
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Antoine Benoit. Geometric optics expansions for hyperbolic corner problems II : from weak stability to violent instability. 2017. ⟨hal-01242899v4⟩

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