Oferta de beca doctoral FPI 2009 Asociada al Proyecto de Investigaci´on MTM2008-06326-C02-01, ”Ecua- ciones de Difusi´on no Lineal y Aplicaciones”, proyecto es financiado por el Ministerio de Ciencia e Innovaci´on (MICINN). Investigador Principal: Juan Luis V´azquez Su´arez. Lugar: Departamento de Matem´aticas de la Universidad Aut´onoma de Madrid. Dedicaci´on: Tiempo completo. Duraci´on: Cuatro a˜ nos. Requisitos: Licenciado en Matem´atica

ANNOUNCEMENT OF FPI SCHOLARSHIP FOR DOCTORAL THESIS Basque Center for Applied Mathematics, Bilbao Research Project: Partial differential equations, analysis, control, numerical approach and applications. Code: MTM2008-03541. Main Researcher: Enrique Zuazua - IKERBASQUE DESCRIPCION OF THE PROJECT. This project is devoted to study some analytical properties of solutions of Partial Differential Equations and its numerical approximation schemes. We shall

Dear friend and colleague, BCAM the newly created Basque Center for Applied Mathematics has just opened an International Call, with the aim of appointing RESEARCHERS on a temporary or permanent basis, in order to carry out research in mathematics, with special emphasis on applied and cross-disciplinary areas. In particular, we are appointing positions for: Ph.D. STUDENTS and POSTDOCTORAL FELLOWS in the areas of: * Partial differential equations,

We consider fully discrete schemes for the one-dimensional linear Schrödinger equation and analyze whether the classical dispersive properties of the continuous model are presented in these approximations. In particular, Strichartz estimates and the local smoothing of the numerical solutions are analyzed. Using a backward Euler approximation of the linear semigroup we introduce a convergent scheme for the nonlinear Schrödinger equation with nonlinearities

This thesis analyzes various numerical schemes for the heat, Schrödinger and wave equations. Our main goal is to describe the behaviour of the solutions of the classical finite difference approximations, focusing on their qualitative properties: decay rates, dispersion, propagation, etc. Our aim is to thoroughly study the dispersion properties of the numerical schemes for the Schrödinger and wave equations, properties which are not only important