Frank Merle

On the Stability of the Notion of Non-Characteristic Point and Blow-Up Profile for Semilinear Wave Equations

We consider a blow-up solution for the semilinear wave equation in N dimensions, with subconformal power nonlinearity. Introducing

Construction of Multi-Solitons for the Energy-Critical Wave Equation in Dimension 5

{\mathcal{R}_0}

Asymptotics for

R0 the set of non-characteristic points with the Lorentz transform of the space-independent solution as asymptotic profile, we show that

minimal blow-up solutions of critical nonlinear Schrödinger equation

{\mathcal{R}_0}

Stability of the blow-up profile of non-linear heat equations from the dynamical system point of view

R0 is open and that the blow-up surface is of class C1 on