920894. Asymptotic Behavior and Dynamics of Differential Equations (CADEDIF)

Facultad de Ciencias Matemáticas

The research team of this UCM Group has been working for more than 20 years with a stable and quality research activity within the area of Applied Mathematics, betwen the Partial Derivative Equations (PDEs) and the Infinite Dimensional Dynamical Systems.
Many important contributions have been made, as evidenced by the number of publications in international journals indexed in the JCR.

Our main targets in the immediate future can be classified into the following thematic blocks that start with a good background of previous results: problems of homogenization and reticulated structures, formation of singularities, non local problems, higher order problems, hyperbolic systems, a priori bounds.

Scientific productivity:

The members of the group maintain a remarkable scientific activity, which is reflected in the published articles. The group has published 193/247 research articles (according to Scopus / Google scholar of the UCM bibliometric Portal) in journals in the area of Mathematics, Applied Mathematics, Multidisciplinary Physics, Multidisciplinary Sciences and Physics-Mathematics. The complete list can also be access in the following database: https://bibliometria.ucm.es/login.

Besides research articles we have published 18 textbooks and / or mathematical dissemination.

The department will provide a suitable office to work in, where it is possible to interact with the rest of postdoc and PhD students.
It will also provide access to the necessary computer facilities, as well as to the extensive collections of the Complutense University Library.

The candidate should have strong expertise in Nonlinear PDEs, mainly of elliptic and parabolic type under both, analytical and numerical point of view. In particular, we are specially interested in the following topics:

Nonlinear parabolic PDEs arising singularities, blow-up/quenching

Numerical analysis of problems arising singularities

Elliptic problems of p-laplacian type when the exponents tend to infinity

Variable exponent and Orlicz type operators

Nonlocal operators with regular kernel: occurence of blow-up/quenching, large solutions, functions of nonlocal least gradient and the nonlocal 1-Laplacian, etc

Nonlocal operators of fractional type and their generalizations to the Orlicz setting

Bifurcation in logistic models

Homogenization processes in fully nonlinear equations

Fully nonlinear equations related to the strong p-laplacian and Tug-Of-War games

Parabolic problems of p-laplacian type when the exponent goes to infinity. Sandplies growth models. Mosco and Gamma convergence of functionals

Numerical analysis of models for sandplies

Elliptic problems with singular potencials of Hardy type

Fourth order equations with singular potential of Rellich type

Opinion formation models and related topics (flocking, swarming,etc). Boltzmann and Fokker-Plank equations with nonlocal transport terms. Wasserstein distance of density measures

Numerical simulation of the discrete equations determining the agent-agent interaction in opinion formation models and related models.

A strong international projection of the candidate, guaranteed by her/his active participation in international conferences, research projects, etc, as well as several years of work experience in high level scientific centers abroad, will be mandatory.

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