Nonlinear Analysis Seminar
Nonlinear Analysis and PDEs
CUNY Graduate Center, 365 Fifth Avenue, NYC
Room 6417, 5:30pm--6:45pm
Goals of these seminars is to discuss techniques that are used nonlinear
problems arising in applied mathematics, physics or differential geometry.
It will also give the opportunity of learning some recent progress in these fields.
Those participating in the Nonlinear Analysis and PDE seminar may
also be interested in the
Geometric Analysis Seminar
which meets also on Thursdays in the same room 6417 starting at 4:15pm.
Spring 2024
July 11 at 2:00pm (in person):
Yihong Du (University of New England, Australia)
On the KPP equation with nonlocal diffusion and free boundaries
Abstract:
A new phenomenon in nonlocal diffusion models is that accelerated propagation may happen, that is,
the propagation speed could be infinite, which never occurs in the corresponding local diffusion model with compactly supported initial data.
In this talk, we will first briefly review the history of the KPP model used to describe the propagation of biological/chemical species, and then look at
some very recent results on the KPP equation with nonlocal diffusion and free boundaries.
For several natural classes of kernel functions appearing in the nonlocal diffusion term, we will show how the exact rate of acceleration can be determined. The talk is based on joint works with Dr Wenjie Ni.
April 18 (in person):
Jianxiong Wang (University of Connecticut)
Higher order conformal equations on hyperbolic spaces and the symmetry of solutions
Abstract:
The classification of solutions for semilinear PDEs, as well as the classification of critical points of the corresponding functionals, have wide applications in the study of partial differential equations and differential geometry. The classical moving plane method and the moving sphere method in Euclidean space provide an
effective approach to capturing the symmetry of solutions.
In this talk, we develop a moving sphere approach for integral equations in the hyperbolic space,
to obtain the symmetry property as well as a characterization result towards positive solutions for nonlinear problems involving the GJMS operators (a generalization of the Paneitz operator). Our methods also rely on Helgason-Fourier analysis and Hardy-Littlewood-Sobolev inequalities on hyperbolic spaces together with a Kelvin transform.
March 28 (in person):
Jesse Ratzkin (Universität Würzburg)
TBA
Abstract: TBA
March 14 (in person):
Lorenzo Sarnataro (Princeton University)
TBA
Abstract: TBA
PAST SEMINARS