Blow-up surfaces for nonlinear wave equations, II

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Abstract
In this second part, we prove that the equation has solutions blowing up near a point of any analytic, space-like hypersurface in , without any additional condition; if is the equation of the surface, is not necessarily analytic, and generally contains logarithmic terms. We then construct singular solutions of general semilinear equations which blow-up on a non-characteristic surface, provided that the first term of an expansion of such solutions can befound. We finally list a few other simple nonlinear evolution equations to which our methods apply; in particular, formal solutions of soliton equations given by a number of authors can be shown to be convergent by this procedure.

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