Oberseminar Mathematik in den Naturwissenschaften: João Henrique Santos de Andrade, Qualitative properties for solutions to subcritical fourth order systems

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.

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