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A decay theorem for some symmetric hyperbolic systems. (English) Zbl 1100.35065

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.

MSC:

35L60 First-order nonlinear hyperbolic equations
35L67 Shocks and singularities for hyperbolic equations
76N15 Gas dynamics (general theory)
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[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
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[9] Morawetz C. S., I. Uspehi Mat. Nauk 29 pp 233–
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