Relaxed formulation and existence result of the degenerated elliptic small disturbance model

✍ Scribed by M. Amara; A. Obeid; G. Vallet

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 276 KB
• Volume: 58
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2004.05.009

✦ Synopsis

We consider an elliptic-parabolic PDE, governing the ow of a steady state two-dimensional irrotational compressible uid in a channel or around a thin proÿle. The model is formulated in term of a noncoercive variational problem with an integral functional, in a truncated domain. We propose a relaxed formulation in the bounded variation functions space and we prove the existence and the uniqueness of the relaxed optimal solution. We consider also the asymptotic behavior of the solution when the domain grows to inÿnity.