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Following our previous paper in the radial case, we consider blow-up type II 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 W concentrating at the origin.
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 univers
We consider the energy supercritical heat equation with the $(n-3)$-th Sobolev exponent begin{equation*} begin{cases} u_t=Delta u+u^{3},~&mbox{ in } Omegatimes (0,T), u(x,t)=u|_{partialOmega},~&mbox{ on } partialOmegatimes (0,T), u(x,0)=u_0(x),~&mbox
We describe the asymptotic behavior of positive solutions $u_epsilon$ of the equation $-Delta u + au = 3,u^{5-epsilon}$ in $Omegasubsetmathbb{R}^3$ with a homogeneous Dirichlet boundary condition. The function $a$ is assumed to be critical in the sen
We prove that any sufficiently differentiable space-like hypersurface of ${mathbb R}^{1+N} $ coincides locally around any of its points with the blow-up surface of a finite-energy solution of the focusing nonlinear wave equation $partial_{tt} u - Del
We prove that the critical Wave Maps equation with target $S^2$ and origin $mathbb{R}^{2+1}$ admits energy class blow up solutions of the form $$u(t,r)=Q(lambda(t)r)+epsilon(t,r)$$where $Q: mathbb{R}^2 to S^2$ is the ground state harmonic map and $la