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2 Annales Polonici Mathematici

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On continuous solutions to linear hyperbolic systems

100%

Zdanowicz M. , Peradzyński Z.

2005

tom 86

nr 3

273-281

We study the conditions under which the Cauchy problem for a linear hyperbolic system of partial differential equations of the first order in two independent variables has a unique continuous solution (not necessarily Lipschitz continuous). In addition to obvious continuity assumptions on coefficients and initial data, the sufficient conditions are the bounded variation of the left eigenvectors along the characteristic curves.

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

100%

Zdanowicz M. , Peradzyński Z.

2013

tom 109

nr 2

177-198

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.