Hyperbolic systems with relaxation: symmetrizers and entropies

This paper deals with the Cauchy problem for hyperbolic so-called stiff systems in one space dimension with large relaxation term depending on a small parameter $delta$. In this case the symmetrizer for the modified symbol of the system, in general, depends on the wave number $omega$ and does not define a quadratic entropy. Therefore, the concept of stiff well-posedness of the Cauchy problem appears. In the paper a mathematical example and a class of physically relevant systems for which the Cauchy problem is stiffly well-posed are considered.