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LOCAL ENERGY DECAY FOR SOLUTIONS OF MULTI-DIMENSIONAL ISOTROPIC SYMMETRIC HYPERBOLIC SYSTEMS

THOMAS C. SIDERIS

Department of Mathematics, University of California, Santa Barbara, CA 93106, USA

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and

BECCA THOMASES

Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA

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https://doi.org/10.1142/S0219891606000975Cited by:21 (Source: Crossref)

Abstract

The local decay of energy is established for solutions to certain linear, multidimensional symmetric hyperbolic systems, with constraints. The key assumptions are isotropy and nondegeneracy of the associated symbols. Examples are given, including Maxwell's equations and linearized elasticity. Such estimates prove useful in treating nonlinear perturbations.

Keywords:

AMSC: 35L45

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