L1 stability for systems of hyperbolic conservation laws with a resonant moving source

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1226-1251
Journal / PublicationSIAM Journal on Mathematical Analysis
Issue number5
Publication statusPublished - 2003


In this paper, we study the L1 stability for the system u t +f(u)x = g(x -ct, u) when one of the characteristic fields has resonance with the moving source. The nonlinear resonance occurs when the speed of the source can coincide with one of the characteristic speeds of the hyperbolic conservation laws, In this situation, a wave pattern can be either stable or unstable. By employing a nonlinear functional approach, we prove the L1 stability of a transonic shock wave under the stability conditions introduced in [W.-C. Lien, Comm. Pure Appl. Math., 52 (1999), pp. 1075-1098; T.-P. Liu, Comm. Math. Phys., 83 (1982), pp. 243-260].

Research Area(s)

  • Hyperbolic conservation laws, L1 nonlinear functional, Resonant source