Suárez Fernández, Antonio

Antonio Suárez is full professor of Mathematical Analysis at US. He obtained his PhD at US in 1999. He has served as Secretary of the Departament of Differential Equations and Numerical Analysis from 2003 to 2004. At present he isCoordinator of the Programme of Doctorate in Mathematics since 2016.
His research has dealt with the theoretical study of nonlinear partial differential equations and systems. Mainly, this research has three main lines:

1.- Models arising in population dynamics: we have studied theoretically nonlinear models arising in population dynamics, focusing our attention on problems where:

a) The diffusion of the species is non-linear, that is, it depends on the population densities. This kind of diffusion appears when the species tries to avoid the agglomeration. This kind of diffusion seems to give more realistic results than those given by linear (random way) diffusion. In this research line, we have colloborated with researchers form the Univerties of Sevilla, Granada, La Laguna, Complutense of Madrid, Campinas and Campina Grande in Brasil.
b) Non-local terms appear. That is, in the classical local partial differential equations, the relation between the unknown and its derivatives are local in space. There are, however, many examples where a global spatial coupling is present in the phenomena and has to be incorporated in the model.
c) Modelization of mutualistic complex networks in Ecology. A mathematical analysis of the relationship between the structural network topology can detect which network topology optimizes biodiversity in mutualistic systems.

 2.- Definition of bifurcation on non-autonomous in time models.

Until now the concept of bifurcation had been defined in autonomous systems, we intend to give a coherent definition of this concept in time-dependent models

3.- Models coming from the growth of tumors. We focused on two thematics:

a) the process of angiogenesis, a fundamental process in tumor growth and subsequent metastasis. We have studied some of these models theoretically and now we are focused on the application to different antiangiogenic therapies.

b) the evolution of a Glioblastoma, one of the more lethal brain tumors. We have analyzed a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes an anisotropic nonlinear diffusion term with a diffusion velocity increasing with respect to vasculature.

We intend to continue advancing in this line, which entails diversifying our research, not only focusing on a purely mathematical training, but also much more applied to medicine and other sciences. 

A. Suárez has been the main research of the Special Program funded by the CNPq (Brazil) in which two Ph. theses were advised (10/2013 – 7/2017).