Blow-up surfaces for nonlinear wave equations, II

Satyanad Kichenassamy, Walter Littman
1993 Communications in Partial Differential Equations  
In this second part, we prove that the equation 2u = e u has solutions blowing up near a point of any analytic, space-like hypersurface in R n , without any additional condition; if (φ(x, t) = 0) is the equation of the surface, u − ln(2/φ 2 ) 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 be
more » ... ch solutions can be found. 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.
doi:10.1080/03605309308820997 fatcat:i7wv5wdz4fbejmw4fojxzyhvxu