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

by Kunik, M.


Preprint series: 04-23, Preprints

76Y05 Quantum hydrodynamics and relativistic hydrodynamics, See also {83C55, 85A30}
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.

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