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Multi-dimensional hyperbolic partial differential equationsFirst-order systems and applications$
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Sylvie Benzoni-Gavage and Denis Serre

Print publication date: 2006

Print ISBN-13: 9780199211234

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780199211234.001.0001

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THE HOMOGENEOUS IBVP

THE HOMOGENEOUS IBVP

Chapter:
(p.182) 7 THE HOMOGENEOUS IBVP
Source:
Multi-dimensional hyperbolic partial differential equations
Author(s):

Sylvie Benzoni-Gavage

Denis Serre

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199211234.003.0007

When the boundary condition is homogeneous, one may think that there is no data at the boundary and that there is no need of boundary estimates in the maximal estimates. This is reminiscent of the case of weakly dissipative symmetric IBVP, and is compatible with the failure of the K.-L. condition at some elliptic boundary frequencies. This chapter constructs a weakly dissipative symmetrizer under appropriate assumptions. This context is the realm of surface waves of finite energy. A paradigm is the Rayleigh waves in linear elasticity.

Keywords:   boundary condition, weakly dissipative symmetrizer, surface waves, Rayleigh waves, K.-L. condition

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