Convergence rate from hyperbolic systems of balance laws to parabolic systems

Abstract

It is proved recently that partially dissipative hyperbolic systems converge globally-in-time to parabolic systems in a slow time scaling, when initial data are smooth and sufficiently close to constant equilibrium states. Based on this result, we establish error estimates between the smooth solutions of the hyperbolic systems of balance laws and those of the parabolic limit systems in one space dimension. The proof of the error estimates uses a stream function technique together with energy estimates. As applications of the results, we give five examples arising from physical models.

COMMUNICATED BY:

• M. Mei

Keywords:

• Convergence rate
• hyperbolic system of balance laws
• partial dissipation
• parabolic system
• stream function

AMS Subject Classifications (2010):

• 35B25
• 35K45
• 35L45

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of this work was supported in part by National Natural Science Foundation of China under grants 11571232, 11831011 and 11671295.