Effect of magnetic activity saturation in chromospheric flux-flux relationships

We present a homogeneous study of chromospheric and coronal flux–flux relationships using a sample of 298 late-type dwarf active stars with spectral types F to M. The chromospheric lines were observed simultaneously in each star to avoid spread as a result of long-term variability. Unlike other works, we subtract the basal chromospheric contribution in all the spectral lines studied. For the first time, we quantify the departure of dMe stars from the general relations. We show that dK and dKe stars also deviate from the general trend. Studying the flux–colour diagrams, we demonstrate that the stars deviating from the general relations are those with saturated X-ray emission and we show that these stars also present saturation in the Hα line. Using several age spectral indicators, we show that these are younger stars than those following the general relationships. The non-universality of flux–flux relationships found in this work should be taken into account when converting between fluxes in different chromospheric activity indicators.

Quenching phenomenon of singular parabolic problems with L1 initial data

We extend some previous existence results for quenching type parabolic problems involving a negative power of the unknown in the equation to the case of merely integrable initial data. We show that L1 Ω is the suitable framework to obtain the continuous dependence with respect to some norm of the initial datum; This way we answer to the question raised by several authors in the previous literature. We also show the complete quenching phenomena for such a L1-initial datum.