Initial-boundary value problem for a compressible dusty gas model

Abstract

Initial-boundary value problem describing one-dimensional two-phase flows of a compressible viscous dusty gas in a channel is considered. Global-in-time unique solvability for small initial data and the exponential decay of the energy for a small total mass of the dust are proved.

Keywords:

• Dusty gas
• Global solvability
• Stability
• AMS Subject Classifications: 35Q35
• 35M20
• 35Q72
• 76N10

Acknowledgement

This work was partially supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNP_q-Brazil).