Geometric optics expansions for hyperbolic corner problems, I: Self-interaction phenomenon

Benoit, Antoine

doi:10.2140/apde.2016.9.1359

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Geometric optics expansions for hyperbolic corner problems, I: Self-interaction phenomenon

Antoine Benoit

Vol. 9 (2016), No. 6, 1359–1418

DOI: 10.2140/apde.2016.9.1359

Abstract

In this article we are interested in the rigorous construction of geometric optics expansions for hyperbolic corner problems. More precisely we focus on the case where self-interacting phases occur. Those phases are proper to the high frequency asymptotics for the corner problem and correspond to rays that can display a homothetic pattern after a suitable number of reflections on the boundary. To construct the geometric optics expansions in that framework, it is necessary to solve a new amplitude equation in view of initializing the resolution of the WKB cascade.

Keywords

hyperbolic corner problem, geometric optics expansions, self-interacting phases

Mathematical Subject Classification 2010

Primary: 35L04, 78A05

Milestones

Received: 28 September 2015

Revised: 15 April 2016

Accepted: 28 May 2016

Published: 3 October 2016

Authors

Antoine Benoit
Université de Nantes Laboratoire de Mathématiques Jean Leray (CNRS UMR6629) 2 rue de la Houssinière BP 92208 44322 Nantes Cedex 3 France

Vol. 9, No. 6, 2016