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Article Dans Une Revue Journal of Differential Equations Année : 1996

Fuchsian equations in Sobolev spaces and blow-up

Satyanad Kichenassamy

Résumé

We construct solutions of $\square u = e^u$ 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.

Dates et versions

hal-00002559 , version 1 (16-08-2004)

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Satyanad Kichenassamy. Fuchsian equations in Sobolev spaces and blow-up. Journal of Differential Equations, 1996, 125, pp.299-327. ⟨10.1006/jdeq.1996.0033⟩. ⟨hal-00002559⟩

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