Relative entropy in hyperbolic relaxation. (English) Zbl 1098.35104

The author consideres the system of hyperbolic equations with the stiff relaxation term: \[ \partial_t U + \sum_\alpha{\partial_\alpha F_\alpha(U)} = \frac{1}{\varepsilon}R(U); \] the system is equipped by a set of conservation laws \(\partial_t PU + \sum_\alpha{\partial_\alpha PF_\alpha(U)}=0\) with non-singular matrix \(P\). The aim of the paper is to produce a relative entropy identity for this general relaxation system. This allows direct proof of convergence theorems.


35L65 Hyperbolic conservation laws
82C40 Kinetic theory of gases in time-dependent statistical mechanics
74D10 Nonlinear constitutive equations for materials with memory
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