Asymptotics of wave models for non star-shaped geometries

Farah Abou Shakra

doi:10.3934/dcdss.2014.7.347

Article Contents

2014, Volume 7, Issue 2: 347-362. Doi: 10.3934/dcdss.2014.7.347

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Asymptotics of wave models for non star-shaped geometries

Farah Abou Shakra^1,

1.
Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS, UMR 7539, F-93430, Villetaneuse

Received: March 31, 2013

Revised: April 30, 2013

Published: March 2014

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Abstract

In this paper, we provide a detailed study and interpretation of various non star-shaped geometries linking them to recent results for the 3D critical wave equation and the 2D Schrödinger equation. These geometries date back to the 1960's and 1970's and they were previously studied only in the setting of the linear wave equation.

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Mathematics Subject Classification: 35L70, 35L20, 35B33, 35Q55.

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