Global behaviour for a viscous, heat-conductive, one-dimensional real gas with a non-autonomous external force and a heat source

Abstract

In this paper, we study the global behaviour for a viscous, heat-conductive, one-dimensional real gas with a non-autonomous external force and a heat source. Under certain assumptions imposed on the initial data and external force, we obtain the global existence of the weak solution, give the uniform bounds (with respect to time) of the solution and show that it converges to a stationary one as time tends to infinity.

Keywords:

• global behaviour
• external force
• initial boundary value

AMS Subject Classifications:

• 35M10
• 35Q30
• 35B40

Acknowledgments

The work is in part supported by Doctoral Foundation of North China University of Water Sources and Electric Power (No. 201087), National Natural Science Foundation of China (No. 11126323) and Innovation Scientists and Technicians Troop Construction Projects of Henan Province.