Control of blow-up singularities for nonlinear wave equations

Satyanad Kichenassamy (1)

1 LMR - Laboratoire de Mathématiques de Reims

While the global boundary control of nonlinear wave equations that exhibit blow-up is generally impossible, we show on a typical example, motivated by laser breakdown, that it is possible to control solutions with small data so that they blow up on a prescribed compact set bounded away from the boundary of the domain. This is achieved using the representation of singular solutions with prescribed blow-up surface given by Fuchsian reduction. We outline on this example simple methods that may be of wider applicability.

Mots clés: blow-up; Fuchsian Reduction; control of singularities

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

Satyanad Kichenassamy. Control of blow-up singularities for nonlinear wave equations. Evolution Equations and Control Theory, 2013, 2 (4), pp.669-677. ⟨10.3934/eect.2013.2.669⟩. ⟨hal-00948959⟩