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:**