TY - JOUR
T1 - Mathematical entropy and Euler-Cattaneo-Maxwell system
AU - Kawashima, Shuichi
AU - Ueda, Yoshihiro
N1 - Publisher Copyright:
© 2016 World Scientific Publishing Company.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - In this paper, we introduce a notion of the mathematical entropy for hyperbolic systems of balance laws with (not necessarily symmetric) relaxation. As applications, we deal with the Timoshenko system, the Euler-Maxwell system and the Euler-Cattaneo-Maxwell system. Especially, for the Euler-Cattaneo-Maxwell system, we observe that its dissipative structure is of the regularity-loss type and investigate the corresponding decay property. Furthermore, we prove the global existence and asymptotic stability of solutions to the Euler-Cattaneo-Maxwell system for small initial data.
AB - In this paper, we introduce a notion of the mathematical entropy for hyperbolic systems of balance laws with (not necessarily symmetric) relaxation. As applications, we deal with the Timoshenko system, the Euler-Maxwell system and the Euler-Cattaneo-Maxwell system. Especially, for the Euler-Cattaneo-Maxwell system, we observe that its dissipative structure is of the regularity-loss type and investigate the corresponding decay property. Furthermore, we prove the global existence and asymptotic stability of solutions to the Euler-Cattaneo-Maxwell system for small initial data.
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U2 - 10.1142/S0219530515400035
DO - 10.1142/S0219530515400035
M3 - Article
AN - SCOPUS:84952909294
VL - 14
SP - 101
EP - 143
JO - Analysis and Applications
JF - Analysis and Applications
SN - 0219-5305
IS - 1
ER -