Nonlinear PDEs and applications

Brief description:

This project concerns on one of the most successful tools of the applied mathematics: Nonlinear Equations Partial and its many applications. Some of the topics considered have a high impact, such as those related to Nanotechnology. Being some of the subjects so new in the mathematical literature, they imply some risk  but its consideration  may be of relevance in the interdisciplinary treatment of so complex field.  This project connects thematically with the European ITN project FIRST (2009-2013) collecting 8 European universities and two multinational companies had as European Coordinator to IP of this project.
The list of objectives suggests the universality of this type of mathematics when  considering problems arising in very different frameworks: Modelling and mathematical treatment of PDEs in Nanotechnology (semiconductors, discrete homogenization of graphene networks, nonlinear Schroedinger and Ginzburg –Landau equations). Diffusion-reaction systems arising in Climatology  and Chemical Engineering). Nonlinear PDEs and stochastic PDEs in Financial Mathematics,  Lithium batteries models,  Application to systems of equations in population studies, Large solutions of nonlinear PDEs, Control of nonlinear PDEs,  etc.


Jesús Ildefonso Díaz Díaz (Professional, Faculty of Mathematics, UCM)
Gregorio Díaz Díaz (Professional, Faculty of Mathematics, UCM)
Jesús Hernández (Professional, Faculty of Mathematics, UAM)
David Gómez Castro (Professional, Faculty of Mathematics, UCM)

Expected Results:

We shall try to publish the results in good journal hoping that the impact of the results will continue (and even improve) the level of citations as in precedents works by the members of the team.