## 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.

### MSC:

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

### Keywords:

relaxation limits; relative entropy
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