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Stability of hydrodynamic model for semiconductor

Massimiliano Daniele Rosini (2005)

Archivum Mathematicum

In this paper we study the stability of transonic strong shock solutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construction of a pseudo-local symmetrizer and on the paradifferential calculus with parameters, which combines the work of Bony-Meyer and the introduction of a large parameter.

Stationary solutions of the generalized Smoluchowski-Poisson equation

Robert Stańczy (2008)

Banach Center Publications

The existence of steady states in the microcanonical case for a system describing the interaction of gravitationally attracting particles with a self-similar pressure term is proved. The system generalizes the Smoluchowski-Poisson equation. The presented theory covers the case of the model with diffusion that obeys the Fermi-Dirac statistic.

Steady tearing mode instabilities with a resistivity depending on a flux function

Atanda Boussari, Erich Maschke, Bernard Saramito (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider plasma tearing mode instabilities when the resistivity depends on a flux function (ψ), for the plane slab model. This problem, represented by the MHD equations, is studied as a bifurcation problem. For so doing, it is written in the form (I(.)-T(S,.)) = 0, where T(S,.) is a compact operator in a suitable space and S is the bifurcation parameter. In this work, the resistivity is not assumed to be a given quantity (as usually done in previous papers, see [1,2,5,7,8,9,10], but it depends...

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