Analysis for time discrete approximations of blow-up solutions of semilinear parabolic equations

We prove a posteriori error estimates for time discrete approximations, for semilinear parabolic equations with solutions that might blow up in finite time. In particular we consider the backward Euler and the Crank–Nicolson methods. The main tools that are used in the analysis are the reconstruction technique and energy methods combined with appropriate fixed point arguments. The final estimates we derive are conditional and lead to error control near the blow up time

Sensitivity to the Higgs sector of SUSY-seesaw models via LFV tau decays

Here we study and compare the sensitivity to the Higgs sector of the SUSY-seesaw models via the LFV tau decays: tau-> 3 mu, tau->K^{+}K^{-}, tau->mu eta and tau-> mu f_{0}. We emphasize that, at present, the two later channels are the most efficient ones to test indirectly the Higgs particles.Comment: 4 pages, 3 figures, conference SUSY09 Boston (M.Herrero

Studying the spectral properties of Active Galactic Nuclei in the JWST era

The James Webb Space Telescope (JWST), due to launch in 2014, shall provide an unprecedented wealth of information in the near and mid-infrared wavelengths, thanks to its high-sensitivity instruments and its 6.5 m primary mirror, the largest ever launched into space. NIRSpec and MIRI, the two spectrographs onboard JWST, will play a key role in the study of the spectral features of Active Galactic Nuclei in the 0.6-28 micron wavelength range. This talk aims at presenting an overview of the possibilities provided by these two instruments, in order to prepare the astronomical community for the JWST era.Comment: 8 pages, 1 figure, accepted for publication in New Astronomy Reviews (proceedings of 7th Serbian Conference on Spectral Line Shapes in Astrophysics

Universality in Blow-Up for Nonlinear Heat Equations

We consider the classical problem of the blowing-up of solutions of the nonlinear heat equation. We show that there exist infinitely many profiles around the blow-up point, and for each integer $k$, we construct a set of codimension $2k$ in the space of initial data giving rise to solutions that blow-up according to the given profile.Comment: 38 page