Asymptotic partial symmetries to reaction-diffusion systems coming from ecology

The interaction between two species can be modeled by a system of two nonlinear reaction-diffusion equations. The equation takes into account the movement of the species, the birth rates, the consequences of concentration, and the interaction between the two populations, which can be cooperative or competitive. These models are sometimes called of Lotka-Volterra type and are complemented with boundary conditions and an initial profile. In this talk, I focus on the shape of solutions for large times; in particular, I show that, under certain assumptions, the solutions exhibit a phenomenon called "asymptotic symmetry", that is, all the elements in the omega-limit set have some kind of symmetry (which depends on the hypothesis), as well as some extra monotonicity properties.

Alberto Saldaña studied Actuarial Sciences in Mexico City at the National Autonomous University of Mexico (UNAM), where he also did his M.S. in Mathematics. He obtained his Ph.D. in Mathematics from the Johann-Wolfgang Goethe-Universität Frankfurt am Main, where he studied qualitative properties of solutions to reaction-diffusion equations. Alberto has done three postdoctoral stays: the first at the Université libre de Bruxelles (ULB) in Belgium, where he studied differential equations of higher-order which model phase separation; the second stay was at the Instituto Superior Técnico (IST) in Portugal, where he studied nonlinear elliptic systems. His third postdoc, with the support of the Alexander von Humboldt Stiftung, was at the Karlsruhe Institut für Technologie (KIT), where his research was focused on the study of quasilinear differential operators used in models of electromagnetism. Also during this period he studied pseudodifferential operators which model processes where the diffusion has jumps.