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A DECAY THEOREM FOR SOME SYMMETRIC HYPERBOLIC SYSTEMS

CATHLEEN S. MORAWETZ

Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, 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/S0219891606000860Cited by:1 (Source: Crossref)

Abstract

In this short note, we consider smooth solutions to certain hyperbolic systems of equations. We present a condition which will ensure that no shocks develop and that solutions decay in L². The condition is restrictive in general; however, when applied to the system of one-dimensional gas dynamics it is shown that if the condition is satisfied initially then it will be satisfied for all time and therefore one obtains smooth solutions which decay.

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