Communications in Mathematical Physics

, Volume 143, Issue 3, pp 599–605 | Cite as

Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping

  • Ling Hsiao
  • Tai-Ping Liu
Article

Abstract

We consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time-asymptotically. The hyperbolic model may be viewed as isentropic Euler equations with friction term added to the momentum equation to model gas flow through a porous media. In this case our result justifies Darcy's law time-asymptotically. Our model may also be viewed as an elastic model with damping.

Keywords

Neural Network Porous Medium Nonlinear Dynamics Parabolic Equation Euler Equation 

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References

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    Nishida, T.: Nonlinear hyperbolic equations and related topics in fluid dynamics. Nishida, T. (ed.) Pub. Math. D'Orsay, 46–53 (1978)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Ling Hsiao
    • 1
  • Tai-Ping Liu
    • 2
  1. 1.Institute of MathematicsAcademia SinicaBeijingChina
  2. 2.Department of MathematicsStanford UniversityStanfordUSA

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