Entropy principle and Relativistic Extended Thermodynamics: Global existence of smooth solutions and stability of equilibrium state

摘要

The entropy principle plays an important role on hyperbolic systems of balance laws: symmetrization, principal subsystems and nesting theories, equilibrium manifold. After a brief survey on these questions we present some recent results concerning the local and global well-posedness of the Cauchy problem for smooth solutions with particular attention to the genuine coupling Kawashima condition. These results are applied to the case of Relativistic Extended Thermodynamics and we prove that there exist global smooth solutions for small initial data and the solutions converge to a constant equilibrium state.