In this paper, we start a general study on relaxation hyperbolic systems which violate the Shizuta–Kawashima coupling condition ([SK]). This investigation is motivated by the fact that this condition is in general not satisfied by various physical systems, and almost all the time in several space dimensions. First, we explore the role of entropy functionals around equilibrium solutions, which may be not constant, proposing a stability condition for such solutions. Then we find strictly dissipative entropy functions for one dimensional 2 × 2 systems which violate [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.

On Relaxation Hyperbolic Systems Violating the Shizuta-Kawashima Condition / Mascia, Corrado; Natalini, Roberto. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 195:(2010), pp. 729-762. [10.1007/s00205-009-0225-x]

On Relaxation Hyperbolic Systems Violating the Shizuta-Kawashima Condition

MASCIA, Corrado;NATALINI, Roberto
2010

Abstract

In this paper, we start a general study on relaxation hyperbolic systems which violate the Shizuta–Kawashima coupling condition ([SK]). This investigation is motivated by the fact that this condition is in general not satisfied by various physical systems, and almost all the time in several space dimensions. First, we explore the role of entropy functionals around equilibrium solutions, which may be not constant, proposing a stability condition for such solutions. Then we find strictly dissipative entropy functions for one dimensional 2 × 2 systems which violate [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.
2010
CONSERVATION LAWS WITH RELAXATION, GLOBAL EXISTENCE, SMOOTH SOLUTIONS,
01 Pubblicazione su rivista::01a Articolo in rivista
On Relaxation Hyperbolic Systems Violating the Shizuta-Kawashima Condition / Mascia, Corrado; Natalini, Roberto. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 195:(2010), pp. 729-762. [10.1007/s00205-009-0225-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/228834
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