Uniform energy decay rates of hyperbolic equations with nonlinear boundary and interior dissipation
Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation
Consider the energy-critical focusing wave equation on the Euclidian space. A blow-up type II solution of this equation is a solution which has finite time of existence but stays bounded in the energy space. The aim of this work is to exhibit universal properties of such solutions. Let be the unique radial positive stationary solution of the equation. Our main result is that in dimension 3, under an appropriate smallness assumption, any type II blow-up radial solution is essentially the sum of...
Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case
Following our previous paper in the radial case, we consider type II blow-up solutions to the energy-critical focusing wave equation. Let W be the unique radial positive stationary solution of the equation. Up to the symmetries of the equation, under an appropriate smallness assumption, any type II blow-up solution is asymptotically a regular solution plus a rescaled Lorentz transform of concentrating at the origin.