A survey for the Muskat problem and a new estimate

This paper shows a summary of mathematical results about the Muskat problem. The main concern is well-posed scenarios which include the possible formation of singularities in finite time or existence of solutions for all time. These questions are important in mathematical physics but also have a strong mathematical interest. Stressing some recent results of the author, we also give a new estimate for the problem in the last section. Initial data with L2 decay and slope less than one provide weak solutions which satisfy a parabolic inequality as in the linear regime.Ministerio de Economía y CompetitividadJunta de Andalucí

Las informaciones de prima de riesgo en la prensa escrita española. Análisis desde una perspectiva lingüística.

Financial news must be translated by journalists in order to be understood by ordinary people. Specially when they are dealing with unusual issues like risk premium. This article examines the language used in those pieces of information from a semantic point of view, related to other text components.La información económica en general y la relacionada con la prima de riesgo, en particular, requieren un especial esfuerzo de traducción por parte de los profesionales que se dedican al periodismo económico. Este artículo se aproxima al estudio del lenguaje de este tipo de textos desde una perspectiva semántica, relacionada con otros elementos periodísticos que ayudan a la configuración del texto

Splash singularities for the one-phase Muskat problem in stable regimes

This paper shows finite time singularity formation for the Muskat problem in a stable regime. The framework we found is with a dry region, where the density and the viscosity are set equal to $0$ (the gradient of the pressure is equal to $(0,0)$) in the complement of the fluid domain. The singularity is a splash-type: a smooth fluid boundary collapses due to two different particles evolve to collide at a single point. This is the first example of a splash singularity for a parabolic problem.Comment: Minor comments added, 26 pages, 1 figur