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The Vice Chancellor for Research and Postgraduate, Dr. Eduardo Notte Cuello, stressed that it seeks to establish a scientific network that enhances training programs for specialized professionals and postgraduates.

Thanks to a collaborative project between the University of La Serena and the University of Tarapacá, it seeks to strengthen the institution's scientific relationships with specialists from other national and foreign organizations, allowing to intensify the training of researchers in Partial Differential Equation Theories and the Application of Control Theories.

This, within the framework of the National Contest of Advanced Human Capital Attraction of Foreigners, Short Stays (Mec) modality of the National Commission of Scientific and Technological Research, CONICYT, which led to the visit to the University of La Serena Doctor of Mathematics , Enrique Fernández Cara, academic and researcher at the University of Seville, Spain.

This project aims to achieve significant advances in research in the area of ​​Non-Linear Analysis, specifically, in the context of nonlinear partial derivative equations (EDPs) and, simultaneously, contribute to the training programs of specialized professionals and postgraduates of the institution.

The Vice Chancellor for Research and Postgraduate of the ULS, Dr. Eduardo Notte, stressed that it seeks to establish a network that consolidates the development and research in the area of ​​Mathematics. “The idea of ​​promoting diverse works in the area of ​​differential equations and control theory. This visit by Professor Enrique Fernández to the ULS, has allowed us to enrich the Doctorate we are teaching in Energy, Water and Environment, through courses and talks associated with his work area, ”he said.

In that sense, the Vice Chancellor added that the initiative allows “to project postgraduate programs in applied Mathematics. These types of visits by relevant researchers help us to shape the cloisters for the programs and to excite the students and academics for these issues ”.

Dr. Marko Rojas Medar, an academic from the University of Tarapacá, a host institution and associated with the University of La Serena in this initiative, said that “there is a lot of work to be done and the mathematical community is still small in Chile. The critical mass in the country in partial differential equations from fluid mechanics is reduced. In Seville there is a strong group on this subject, and in recent years we have received several visiting professors from the aforementioned house of studies as well as several teachers from Chile we have been received there, developing a synergy, which I think has already begun to give its fruits We believe that we are planting the bases, in the ULS, so that in the future programs of Magister and Doctorates are created, in the area of ​​Applied Mathematics, in particular in the study of physical phenomena governed by Equations in Partial Derivatives ”.

For his part, Dr. Enrique Fernández, explained that with this visit he seeks to deepen scientific aspects in Partial Differential Equation Theories and the application of Control Theories that serve to govern the behavior of the equations, developing an applied component.

“These formulas serve to represent phenomena of all kinds, if they work well enough. It is possible, for example, to determine the flow of a river, and how its particles behave, by solving certain equations in which data can be measured, so that the movement of the river is ascertained. This can be important to know the spread of a contamination or if we are in a time of floods or drought, it has endless applications, ”he explained.

In medicine, for example, Dr. Fernández added that the importance of Partial Differential Equations would allow the study of the evolution of a tumor. "In mathematics, models can be developed to determine the behavior of a tumor in the presence of adequate therapy."

In that same area, the Control Theory would determine what data and circumstances are appropriate for the solution to be expected. "Taking the example of the tumor, this allows obtaining optimal therapies."

Dr. Fernández explained that in this visit specifically, it is expected to obtain results emphasizing problems linked to the magnetohydrodynamic equations, equations that allow the study of the movement of fluids that are subject to electromagnetic effects. “The evolution of the fluid depends a lot on the electric charges in the environment, and we are dedicated to its resolution and subsequent control, in the sense of determining conditions that make the fluid meet good priorities. A practical example is a fluid around an airplane that, due to different atmospheric effects, can be charged with electricity, and the equations help to describe the possible turbulence or instability that may be generated. The Control Theory in this case, can contribute to the design of the aircraft and minimize these effects. ”

The visit of the researcher to the University of La Serena, has a positive impact on the Bachelor and Master's students in Mathematics, due to open seminars and exhibitions. On the other hand, it allows the possibility of teacher improvement, in addition to deepening learning in a specialty area and integrating into research groups currently integrated by Dr. Fernández internationally and nationally. Another positive aspect has been to conclude some research papers, which will be sent to high-impact journals, as well as start new work together.

Written by Sergio Muñoz, Science and Technology Outreach and Dissemination Team