Fuchsian Equations in Sobolev Spaces and Blow-Up

Author: Kichenassamy S.

Source: Journal of Differential Equations, Volume 125, Number 1, February 1996 , pp. 299-327(29)

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Abstract:

We construct solutions of □ u = 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.

Language: English

Document Type: Research article

Affiliations: School of Mathematics, Univesity of Minnesota, 127 Vincent Hall, 206 Church Street S.E., Minneapolis, Minnesota, 55455-0487

Publication date: 1996-02-01