Morawetz, Cathleen S.; Thomases, Becca A decay theorem for some symmetric hyperbolic systems. (English) Zbl 1100.35065 J. Hyperbolic Differ. Equ. 3, No. 3, 475-480 (2006). The authors present a decay result for symmetric hyperbolic \(m\times n\) systems which satisfy certain conditions. It is also shown that certain estimates at \(t=0\) remain for all \(t\). The result relies on spatial, time, and scaling invariance. An example is presented: the one-dimensional gas dynamics system. Reviewer: Ilya A. Chernov (Petrozavodsk) Cited in 1 Document MSC: 35L60 First-order nonlinear hyperbolic equations 35L67 Shocks and singularities for hyperbolic equations 76N15 Gas dynamics (general theory) Keywords:hyperbolic systems; decay; gas dynamics; smooth solutions; symmetric hyperbolic \(m\times n\) systems; scaling invariance PDFBibTeX XMLCite \textit{C. S. Morawetz} and \textit{B. Thomases}, J. Hyperbolic Differ. Equ. 3, No. 3, 475--480 (2006; Zbl 1100.35065) Full Text: DOI References: [1] DOI: 10.1007/s00205-003-0291-4 · Zbl 1055.78003 · doi:10.1007/s00205-003-0291-4 [2] DOI: 10.1063/1.1621057 · Zbl 1063.81042 · doi:10.1063/1.1621057 [3] DOI: 10.1090/ulect/002 · doi:10.1090/ulect/002 [4] DOI: 10.1090/S0894-0347-03-00443-0 · Zbl 1055.35075 · doi:10.1090/S0894-0347-03-00443-0 [5] DOI: 10.1002/cpa.3160380305 · Zbl 0635.35059 · doi:10.1002/cpa.3160380305 [6] DOI: 10.1063/1.1704154 · Zbl 0135.15101 · doi:10.1063/1.1704154 [7] DOI: 10.1090/S0002-9939-03-07246-0 · Zbl 1061.35053 · doi:10.1090/S0002-9939-03-07246-0 [8] Metcalfe J., Houston J. Math. 30 pp 259– [9] Morawetz C. S., I. Uspehi Mat. Nauk 29 pp 233– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.