Geodesic
Propagation of weak discontinuities for quasilinear hyperbolic systems with coefficients functionally dependent on solutions
Małgorzata Zdanowicz1 ; Zbigniew Peradzyński2
1 Institute of Mathematics University of Białystok 15-267 Białystok, Poland
2 Institute of Mathematics Warsaw University 02-097 Warszawa, Poland
Annales Polonici Mathematici, Tome 109 (2013) no. 2, pp. 177-198.

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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.
DOI : 10.4064/ap109-2-6
Keywords: propagation weak discontinuities quasilinear systems coefficients functionally dependent solution studied demonstrate similarly usual quasilinear systems transport equation intensity weak discontinuity quadratic intensity however contribution nonlocal functional dependence appears principle linear jump intensity exceptions illustration several examples including hyperbolic systems functional dependence dispersive maxwell equations fluid equations hall plasma thruster considered

Małgorzata Zdanowicz 1 ; Zbigniew Peradzyński 2

1 Institute of Mathematics University of Białystok 15-267 Białystok, Poland
2 Institute of Mathematics Warsaw University 02-097 Warszawa, Poland 
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Małgorzata Zdanowicz; Zbigniew Peradzyński. Propagation of weak discontinuities for
 quasilinear hyperbolic systems with
 coefficients functionally dependent on solutions. Annales Polonici Mathematici, Tome 109 (2013) no. 2, pp. 177-198. doi : 10.4064/ap109-2-6. http://geodesic.mathdoc.fr/articles/10.4064/ap109-2-6/

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