Nonlinearity, Complexity and Foundations in Mathematics
timetable:
Thu 12 Sep, 17:00 - 17:35, Aula Dini
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Limiting profiles for a Schr ̈odinger equation with a shrinking region of attraction
speaker: Monica Clapp (Universidad Nacional Autónoma de México)abstract: We study the existence and concentration behavior of solu- tions to a Schr ̈odinger equation in the presence of a shrinking self-focusing
core of arbitrary shape. After rescaling, the concentration gives rise to a li- miting profile that solves a nonautonomous semilinear elliptic equation with
a sharp sign change in the nonlinearity. We establish some qualitative properties (symmetries and asymptotic decay) of the limiting profiles, and present further existence results for the limiting equation. It is the product of collaborations with V ́ıctor Hern ́andez-Santamar ́ıa (UNAM), Angela Pistoia (Sapienza) and Alberto Salda ̃na (UNAM).
timetable:
Thu 12 Sep, 17:00 - 17:35, Aula Dini
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