The existence and convergence of the Maxwell model for granular materials

Abstract

In this paper, we study the pseudo-Maxwell model for granular materials, we prove the existence of a solution to this model. Under some hypotheses on the initial data, for all time , the solution belongs to Schwartz’s space of rapidly decreasing smooth functions. In addition, we prove that the solution converges exponentially to the steady state when in some Sobolev space .

Keywords:

• Granular material
• pseudo-Maxwell model
• inelastic Boltzmann equation

AMS Subject Classifications:

• 76T25
• 76P05

Acknowledgements

The author would like to express their sincere thanks to the referees for valuable comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11401318]; the Natural Science Foundation of the Jiangsu Higher Education Institutions of China [grant number 14KJB110020]; the Scientific Research Foundation of NUPT [grant number NY214023].