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Mathematical entropy and Euler-Cattaneo-Maxwell system. (English) Zbl 1336.35226

The authors consider multidimensional hyperbolic balance laws with asymmetrical relaxation. The mathematical concept of entropy is modified for this class. The dissipative Timoshenko system and the isentropic Euler-Maxwell system with frictional damping are considered as examples. Then the Euler-Cattaneo-Maxwell system with frictional damping is proposed and studied. In particular, global existence and asymptotic stability for small initial data in Sobolev space is established, dissipative structure is shown to be of the regularity-loss type.

MSC:

35L60 First-order nonlinear hyperbolic equations
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35Q31 Euler equations
35Q61 Maxwell equations
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