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Geometric optics expansions for linear hyperbolic boundary value problems and optimality of energy estimates for surface waves. (English) Zbl 1340.35186
Summary: 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.

35L04 Initial-boundary value problems for first-order hyperbolic equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
78A05 Geometric optics