Analysis of a Poisson system with boundary conditions
François Castella, Philippe Chartier, Erwan Faou · Comptes Rendus Mathématique · 2003
We consider a class of problems originating from a Raman laser amplification model, for which the equations can be written as a Poisson system with boundary conditions. Once reformulated, this system becomes an integro-differential equation that we study here in some detail. In particular, we show the existence of a smooth solution under general assumptions, and prove its uniqueness for boundary values that are not too far apart. Eventually, we completely solve the question of uniqueness for systems of dimensions one and two.