Differential and Integral Equations

Geometric optics expansions for linear hyperbolic boundary value problems and optimality of energy estimates for surface waves

Antoine Benoit

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this article we are interested in energy estimates for hyperbolic initial boundary value problem when surface waves occur. More precisely, we construct rigorous geometric optics expansions for so-called elliptic and mixed frequencies and we show, using those expansions, that the amplification phenomenon is greater in the case of mixed frequencies. As a consequence, this result allow us to give a partial classification of weakly well-posed hyperbolic initial boundary value problems according to the region where the uniform Kreiss Lopatinskii condition degenerates.

Article information

Source
Differential Integral Equations, Volume 27, Number 5/6 (2014), 531-562.

Dates
First available in Project Euclid: 3 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1396558096

Mathematical Reviews number (MathSciNet)
MR3189531

Zentralblatt MATH identifier
1340.35186

Subjects
Primary: 35L04: Initial-boundary value problems for first-order hyperbolic equations 78A05: Geometric optics

Citation

Benoit, Antoine. Geometric optics expansions for linear hyperbolic boundary value problems and optimality of energy estimates for surface waves. Differential Integral Equations 27 (2014), no. 5/6, 531--562. https://projecteuclid.org/euclid.die/1396558096


Export citation