BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Susanna Terracini (Università di Torino) DTSTART:20201026T140000Z DTEND:20201026T150000Z DTSTAMP:20260423T035910Z UID:SNPDEA/15 DESCRIPTION:Title: Segregation\, interaction of species and related free boundary problems\nby Susanna Terracini (Università di Torino) as part of "Partial Differ ential Equations and Applications" Webinar\n\n\nAbstract\nReaction-diffusi on systems with strong interaction terms appear in many multi-species phy sical problems as well as in population dynamics\, chemistry and material science. The qualitative properties of the solutions and their limiting pr ofiles in different regimes have been at the center of the community's att ention in recent years. A prototypical example appears when looking for so litary wave solutions for Bose-Einstein condensates of two (or more) diffe rent hyperfine states which overlap in space. Typically the forces between particles in the same state are attractive while those between particles in different states can be either attractive or repulsive. If the condensa tes repel\, they eventually separate spatially giving rise to a free boun dary. This phenomenon is called phase separation and has been described in recent literature\, both physical and mathematical. \n\nOne of the most interesting problems researchers investigate is when different phases of m atter\, populations\, or clusters exist in a single space (i.e. in adjacen t cells). Their interest focuses not only in how these different phases/p opulations/clusters interact with one another\, but also on the properties of the boundaries separating them. The recent literature shows that the w alls separating the different phases are geometrically tractable surfaces\ , as well as multiple junctions among them. This involves developing novel variational methods and geometric measure theory and free boundary tools. Relevant connections have been established with optimal partition proble ms involving spectral functionals. The classification of entire solutions and the geometric aspects of the nodal sets of solutions are of fundament al importance as well. We intend to focus on the most recent development o f the theory in connection with problems featuring anomalous diffusions\, long-range and non symmetric.\n LOCATION:https://researchseminars.org/talk/SNPDEA/15/ END:VEVENT END:VCALENDAR