On Relaxation Hyperbolic Systems Violating the Shizuta-Kawashima Condition

Abstract
In this paper, we start a general study on relaxation hyperbolic systems which violate the Shizuta-Kawashima ([SK]) coupling condition. This investigation is motivated by the fact that this condition is not satisfied by various physical sys- tems, and almost all the time in several space dimensions. First, we explore the role of entropy functionals around equilibrium solutions, which may not be constant, proposing a stability condition for such solutions. Then we find strictly dissipa- tive entropy functions for one dimensional 2 × 2 systems which violate the [SK] condition. Finally, we prove the existence of global smooth solutions for a class of systems such that condition [SK] does not hold, but which are linearly degenerated in the non-dissipative directions.
Anno
2010
Autori IAC
Tipo pubblicazione
Altri Autori
Mascia C.; Natalini R.
Editore
Springer.
Rivista
Archive for rational mechanics and analysis (Print)