Asymptotic Behavior for Scalar Viscous Conservation Laws with Boundary Effect

✍ Scribed by Tai-Ping Liu; Kenji Nishihara

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 688 KB
• Volume: 133
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1996.3217

✦ Synopsis

We consider the asymptotic stability of viscous shock wave , for scalar viscous conservation laws

Our problem is divided into three cases depending on the sign of shock speed s of the shock (u & , u + ). When s 0, the asymptotic state of u becomes ,( } +d(t)), where d(t) depends implicitly on the initial data u(x, 0) and is related to the boundary layer of the solution at the boundary x=0. The stability of this state for s<0 will be shown by applying the weighted energy method. For s=0 a conjecture on d(t) will be presented. The case s>0 is also treated.

1997 Academic Press where f (u) # C 2 for all u under consideration. Without loss of generality, assume f (u & )=0. In the simplified situation where f (u) is convex and article no. DE963217 296 0022-0396Â97 25.00