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Large Time Behavior of Solutions for General Quasilinear Hyperbolic-Parabolic Systems of Conservation Laws
Tai-Ping LiuYanni Zeng
出版American Mathematical Soc., 1997
主題Mathematics / GeneralMathematics / Differential Equations / GeneralMathematics / Differential Equations / PartialScience / Waves & Wave Mechanics
ISBN08218054529780821805459
URLhttp://books.google.com.hk/books?id=h4DTCQAAQBAJ&hl=&source=gbs_api
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註釋We are interested in the time-asymptotic behavior of solutions to viscous conservation laws. Through the pointwise estimates for the Green's function of the linearized system and the analysis of coupling of nonlinear diffusion waves, we obtain explicit expressions of the time-asymptotic behavior of the solutions. This yields optimal estimates in the integral norms. For most physical models, the viscosity matrix is not positive definite and the system is hyperbolic-parabolic, and not uniformly parabolic. This implies that the Green's function may contain Dirac [lowercase Greek]Delta-functions. When the corresponding inviscid system is non-strictly hyperbolic, the time-asymptotic state contains generalized Burgers solutions. These are illustrated by applying our general theory to the compressible Navier-Stokes equations and the equations of magnetohydrodynamics.