Acta mathematica scientia, Series B >
ON GREEN'S FUNCTION FOR HYPERBOLIC-PARABOLIC SYSTEMS
Received date: 2009-10-25
Online published: 2009-11-20
Supported by
The research of the first author was partially supported by NSC Grant 96-2628-M-001-011 and NSF Grant DMS-0709248. The research of the second author was partially supported by NSF Grant DMS-0207154.
We study the Green's function for a general hyperbolic-parabolic system, including the Navier-Stokes equations for compressible fluids and the equations for magnetohydrodynamics. More generally, we consider general systems under the basic Kawashima-Shizuta type of
conditions. The first result is to make precise the secondary waves with subscale structure, revealing the nature of coupling of waves
pertaining to different characteristic families. The second result is on the continuous differentiability of the Green's function with
respect to a small parameter when the coefficients of the system are smooth functions of that parameter. The results significantly improve previous results obtained by the authors.
Tai-Ping Liu , Yanni Zeng . ON GREEN'S FUNCTION FOR HYPERBOLIC-PARABOLIC SYSTEMS[J]. Acta mathematica scientia, Series B, 2009 , 29(6) : 1556 -1572 . DOI: 10.1016/S0252-9602(10)60003-3
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