Large Time Behavior of Solutions for General Quasi-linear Hyperbolic-Parabolic Systems of Conservation Laws. Volume 125, Number 599

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  • Large Time Behavior of Solutions for General Quasi-linear Hyperbolic-Parabolic Systems of Conservation Laws. Volume 125, Number 599 Book Detail

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  • Release Date : 1997
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  • Pages : 0
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  • File Size : 60,60 MB
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Large Time Behavior of Solutions for General Quasi-linear Hyperbolic-Parabolic Systems of Conservation Laws. Volume 125, Number 599 by PDF Summary

Book Description: 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-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.

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Navier–Stokes Equations

Navier–Stokes Equations

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Originally published in 1977, the book is devoted to the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluid. On the t