Oberseminar Mathematik in den Naturwissenschaften: João Henrique Santos de Andrade, Qualitative properties for solutions to subcritical fourth order systems
|Date:||06/30/2021, 2:15 PM - 3:45 PM|
|Organizer:||Lehrstuhl für Mathematik VI (Mathematik in den Naturwissenschaften)|
|Speaker:||Universidade de São Paulo - USP, Instituto de Matemática e Estatı́stica Departamento de Matemática|
via Zoom video conference (request the Zoom link from firstname.lastname@example.org).
In this talk we prove some qualitative properties of singular solutions to a class of strongly coupled systems involving a Gross–Pitaevskii-type nonlinearity. On the technical level, we use the moving sphere method to classify the limit blow-up solutions to our system. Additionally, applying asymptotic analysis techniques, we show that these solutions are indeed the local models near the isolated singularity. We also introduce a new fourth order nonautonomous Pohozaev functional, whose monotonicity properties yield improvement for the asymptotics results due to R. Soranzo.