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2004-23

Selected Initial and Boundary Value Problems for Hyperbolic Systems and Kinetic Equations

by Kunik, M..


Series: 2004-23, Preprints

MSC:
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
82C40 Kinetic theory of gases
82C70 Transport processes

Abstract:
We aim to combine a mathematical study
of hyperbolic systems and conservation laws
with specific applications in physics.
The main part of this work will consider
applications to Lorentz-invariant systems,
namely for the Maxwell equations and the
relativistic Euler equations.
But we will also study the so called Boltzmann-Peierls equation,
a kinetic equation for a phonon-Bose gas
describing heat conduction in a dielectric solid at very low temperature,
and a hyperbolic system resulting from this kinetic equation
as a special limiting case.
We will see that the latter system shows a deep mathematical
relationship to the so called ultra-relativistic Euler equations,
though the physical applications are totally different in both cases.

Keywords: