Finite speed of propagation for mixed problems in the $WR$ class

Antoine Benoit

doi:10.3934/cpaa.2014.13.2351

Article Contents

2014, Volume 13, Issue 6: 2351-2358. Doi: 10.3934/cpaa.2014.13.2351

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Finite speed of propagation for mixed problems in the $WR$ class

Antoine Benoit^1,

1.
Université de Nantes, Laboratoire de Mathématiques Jean Leray (CNRS UMR6629), 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3

Received: September 30, 2013

Revised: February 28, 2014

Published: October 2014

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Abstract

In this article we are interested in the propagation speed for solutions of hyperbolic boundary value problems in the $WR$ class. Using the Holmgren principle, we show that this speed is finite and we are able to give an explicit expression for the maximal speed. Due to a propagation phenomenon along the boundary that is specific to the $WR$ class, the maximal speed can be larger than the propagation speed for the Cauchy problem. This is consistent with previous examples of the litterature.

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Mathematics Subject Classification: Primary: 35L50.

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