Stress and heat flux stabilization for viscous compressible medium equations with a nonmonotone state function

✍ Scribed by A.A. Zlotnik

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 452 KB
• Volume: 16
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(03)90122-4

✦ Synopsis

we study a system of quasilinear equations describing one-dimensional flow of a viscous compressible heat-conducting medium with a nonmonotone state function and mass force. The large-time behavior of solutions is considered for arbitrarily large initial data. In spite of possible nonuniqueness and discontinuity of the stationary solution, we prove L2-stabilization for the stress and heat flux as t -+ 00 along with corresponding global energy estimates for them. The new method of proof utilizes a combination of energy type equalities for the stress and heat flux. Consequently, H'-stabilization of the velocity and temperature along with global estimates for their derivatives are valid as well.