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H-measures applied to symmetric systems*

Published online by Cambridge University Press:  14 November 2011

Nenad Antonić
Nenad Antonić
Affiliation:
Department of Mathematics, University of Zagreb, Bijenička cesta 30, Zagreb, Croatia e-mail: nantonic@srce.hr
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Abstract

H-measures were recently introduced by Luc Tartar as a tool which might provide better understanding of propagating oscillations. Independently, Patrick Gerard introduced the same objects under the name of microlocal defect measures. Partial differential equations of mathematical physics can often be written in the form of a symmetric system:

where Ak and B are matrix functions, while u is an unknown vector function, and f a known vector function. In this work we prove a general propagation theorem for H-measures associated to symmetric systems. This result, combined with the localisation property, is then used to obtain more precise results on the behaviour of H-measures associated to the wave equation, Maxwell's and Dirac's systems, and second-order equations in two variables.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 6 , 1996 , pp. 1133 - 1155
Copyright
Copyright © Royal Society of Edinburgh 1996

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