Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 101-143 |
| Number of pages | 43 |
| Journal | Analysis and Applications |
| Volume | 14 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 1 2016 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Cite this
Mathematical entropy and Euler-Cattaneo-Maxwell system. / Kawashima, Shuichi; Ueda, Yoshihiro.
In: Analysis and Applications, Vol. 14, No. 1, 01.01.2016, p. 101-143.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Mathematical entropy and Euler-Cattaneo-Maxwell system
AU - Kawashima, Shuichi
AU - Ueda, Yoshihiro
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.
UR - http://www.scopus.com/inward/record.url?scp=84952909294&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84952909294&partnerID=8YFLogxK
U2 - 10.1142/S0219530515400035
DO - 10.1142/S0219530515400035
M3 - Article
VL - 14
SP - 101
EP - 143
JO - Analysis and Applications
JF - Analysis and Applications
SN - 0219-5305
IS - 1
ER -