Seminario

Seminario Análisis y EDPs

Finding quasiperiodic solutions of elliptic equations on the entire space using center manifold and KAM theorems

Ponente:  Peter Polacik (School of Mathematics, University of Minnesota)
Fecha:  miércoles 23 de febrero de 2022 - 15:00
Online:  s06web.zoom.us/j/81491079139?pwd=OWo1TWc0NEExNDJZUFljWVRIdkZRQT09 (ID: 814 9107 9139; Access code: 937701)

Resumen:

We consider positive solutions of nonlinear elliptic equations on the (N+1)-dimensional Euclidean space with some predetermined behavior (such as decay and symmetry) in the first N variables. We examine the behavior of these solutions in the remaining variable. Families of solutions periodic in the last variable have been found by several authors; our goal is to prove the existence of quasiperiodic solutions. For this purpose, we examine the spatial dynamics of the equation on a center manifold and apply KAM-type results. In the lecture, I will outline our general techniques and report on recent progress. This is joint work with Dario Valdebenito.