Fuchsian Equations in Sobolev Spaces and Blow-Up

✍ Scribed by Satyanad Kichenassamy

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 727 KB
• Volume: 125
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1996.0033

✦ Synopsis

We construct solutions of gu=e u which blow-up precisely on a given space-like hypersurface of class H s . For this purpose, we prove a general existence theorem for Fuchsian PDE in Sobolev spaces. The precise relation between the regularity of the data and that of the solution is shown to involve logarithmic symbols, in a model situation. A few further results on power nonlinearities are also included. 1996 Academic Press, Inc. where 1. N is a first-order operator of the form, 0 i, j l m ij t j  t i , 2. x # R n , uÁ # R P , and the matrices A and M :=(m ij ) are constant, 3. f =O(|t| ) near t=0.