Blow-up surfaces for nonlinear wave equations, Part I

Satyanad Kichenassamy (1) , Walter Littman (1)

1 UMN-MATH - School of Mathematics

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 2u = exp(u); we find necessary and sufficient conditions for the existence of a solution of the form ln(2/φ 2) + v, where {φ = 0} is the blow-up surface, and v is analytic. This gives a natural way of continuing solutions after blow-up.

Domaines: Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]

Satyanad Kichenassamy, Walter Littman. Blow-up surfaces for nonlinear wave equations, Part I. Communications in Partial Differential Equations, 1993, 18 (3-4), pp.431-452. ⟨10.1080/03605309308820936⟩. ⟨hal-00002668⟩