Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.
DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.
Continuing the investigations started in the recent work [12] on semi-global controllability and stabilization of the (1+1)-dimensional wave maps equation with spatial domain S1 and target Sk , where semi-global refers to the 2π-energy bound, we prov ...
We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the scaling parameter λ(t)=t−1−ν is sufficiently close to ...
We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation [ \Box u = -u^5 ] on R3+1 constructed in [28], [27] are stable along a co-dimension three manifold of radial data perturbations in a suit ...
We construct a center-stable manifold of the ground state solitons in the energy space for the critical wave equation without imposing any symmetry, as the dynamical threshold between scattering and blow-up, and also as a collection of solutions which stay ...
We consider radially symmetric, energy critical wave maps from (1 + 2)-dimensional Minkowski space into the unit sphere Sm, m≥1, and prove global regularity and scattering for classical smooth data of finite energy. In addition, we establish a ...
We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation [ \Box u = -u^5 ] on R3+1 constructed in \cite{KST}, \cite{KS1} are stable along a co-dimension one Lipschitz manifold of data perturbations in a ...
We exhibit non-equivariant perturbations of the blowup solutions constructed in [18] for energy critical wave maps into S2. Our admissible class of perturbations is an open set in some sufficiently smooth topology and vanishes near the light co ...
We study the Cauchy problem for the one-dimensional wave equation \[ \partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0. \] The potential V is assumed to be smooth with asymptotic behavior \[ V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty. \] ...
We investigate the stability and stabilization of the cubic focusing Klein-Gordon equation around static solutions on the closed ball in R3. First we show that the system is linearly unstable near the static solution u≡1 for any dissipat ...
In this paper we consider the equation for equivariant wave maps from R3+1 to S-3 and we prove global in forward time existence of certain C-infinity-smooth solutions which have infinite critical Sobolev norm (H) overdot(3/4) (R-3) x (H) overdot(1/2) (R-3) ...
