Spiralling asymptotic profiles of competition-diffusion systems

In this talk we consider solutions of the competitive elliptic system $$ \begin{cases} -\Delta u_i = - \beta \sum_{j \neq i} a_{ij} u_i u_j & \text{in $\Omega\subset \mathbb{R}^2$} \\ u_i =g & \text{in $\partial\Omega$} \end{cases} \qquad i=1,\dots,k, $$ and their asymptotic profiles when $\beta\to+\infty$. We shall focus our attention on the asymmetric case: $a_{ij}\neq a_{ji}$. This is a joint result with A. Salort, S. Terracini, A. Zilio.Non UBCUnreviewedAuthor affiliation: Politecnico di MilanoFacult