On the regularity of the blow-up set for semilinear heat equations
Blow-up results for vector-valued nonlinear heat equations with no gradient structure
Estimations uniformes à l’explosion pour les équations de la chaleur non linéaires et applications
Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension
We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution , the graph of its blow-up points and the set of all characteristic points and show that is locally finite. Finally, given , we show that in selfsimilar variables, the solution decomposes into a decoupled sum of (at least two) solitons, with alternate signs and that forms a...
Page 1