Propagation of weak discontinuities for quasilinear hyperbolic systems with coefficients functionally dependent on solutions

Volume 109 / 2013

Małgorzata Zdanowicz, Zbigniew Peradzyński Annales Polonici Mathematici 109 (2013), 177-198 MSC: 35A21, 35R10, 58J47. DOI: 10.4064/ap109-2-6


The propagation of weak discontinuities for quasilinear systems with coefficients functionally dependent on the solution is studied. We demonstrate that, similarly to the case of usual quasilinear systems, the transport equation for the intensity of weak discontinuity is quadratic in this intensity. However, the contribution from the (nonlocal) functional dependence appears to be in principle linear in the jump intensity (with some exceptions). For illustration, several examples, including two hyperbolic systems (with functional dependence), the dispersive Maxwell equations and fluid equations of the Hall plasma thruster, are considered.


  • Małgorzata ZdanowiczInstitute of Mathematics
    University of Białystok
    15-267 Białystok, Poland
  • Zbigniew PeradzyńskiInstitute of Mathematics
    Warsaw University
    02-097 Warszawa, Poland

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