Blow-up Surfaces for Nonlinear Wave Equations, I
- 1 January 1993
- journal article
- research article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 18 (3-4) , 431-452
- https://doi.org/10.1080/03605309308820936
Abstract
We introduce a systematic procedure for reducing nonlinear wave equations to characteristic problems of Fuchsian type. This reduction is combined with an existence theorem to produce solutions blowing up on a prescribed hypersurface. This first part develops the procedure on the example □u = exp(u); we find necessary and sufficient conditions for the existence of a solution of the form ln(2/⊘2) + v, where {⊘ = 0} is the blow-up surface, and v is analytic. This gives a natural way of continuing solutions after blow-up.Keywords
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