Geometric Analysis and PDE Seminar
Ohsang Kwon (Center for PDE, East China Normal University)
The effects of starvation driven diffusion on the dynamics of populations
ABSTRACT.
The dispersal strategies of biological organisms are key ingredients in
their ecological evolution. It is well-accepted that spatial and temporal heterogeneities of environments occur in all scales and such heterogeneities play
a key role in the evolutional selection of dispersal rates. Recently, starvation
driven diffusion has been introduced by Cho and Kim (Bull. Math. Biol.,
75 (2013) 845-870), which is a random dispersal strategy with a motility
increase on starvation. In this talk, we will discuss properties of the single
species model and 2 2 competition model with starvation driven diffusion,
including the global asymptotic stability and the acquisition of the ideal free
distribution. We show that such a dispersal strategy has fitness property
and that the evolutional selection favors fitness but not simply slowness.
This is the joint work with Y.-J. Kim and F. Li.
Soojung Kim (NIMS)
Harnack inequality for nondivergent parabolic operators on Riemannian manifolds
ABSTRACT.
In this talk, I will discuss the Krylov-Safonov theory which is the analogue of the De Giorgi-Nash-Moser theory.
In particular, I will explain the Krylov-Safonov Harnack inequality for parabolic operators on certain
Riemannian manifolds. This result gives a new nondivergent proof for the Li-Yau Harnack inequality of the heat
equation on manifolds with nonnegative Ricci curvature.
This talk is based on a joint work with Seick Kim and Ki-Ahm Lee.
Seunghyeok Kim (KAIST)
Introduction to Lyapunov-Schmidt reduction method and its applications to various problems.
ABSTRACT.
Since the seminal work of Floer and Weinstein in 1986, the Lyapunov-Schmidt reduction method has served as one of the powerful method to
construct various type of solutions for equations arising mainly from physics and geometry, which leads a plethora of striking results.
Throughout the talk, I will introduce the main idea of the reduction method and its applications to nonlinear Schrödinger equations,
Allen-Cahn equations and so on.
Jinmyoung Seok (KIAS)
Equivalence of the Chern-Simons-Schrodinger equations and its first order self-dual systems
ABSTRACT.
The aim of this talk is to give a rigorous proof of the equivalence of the second order CSS equations to its
first order self-dual systems when a coupling constant is critical.
Juhi Jang (University of California, Riverside)
Stability theory of polytropic gaseous stars
ABSTRACT.
I'll discuss stability theory of Lane-Emden equilibrium stars under Euler-Poisson or Navier-Stokes-Poisson system.
A linear stability can be characterized by the adiabatic exponent.
A nonlinear instability will be also discussed.
TOPICS Differential Geometry - Geometric Analysis - PDE ORGANIZERS Hyunsuk KANG - Korea Institute for Advanced Study Youngju KIM - Korea Institute for Advanced Study Hojoo LEE - Korea Institute for Advanced Study Leobardo ROSALES - Korea Institute for Advanced Study Jinmyoung SEOK - Korea Institute for Advanced Study Keomkyo SEO - Sookmyung Women's Univ. How to visit KIAS Directions to KIAS English - Korean
View KIAS in a larger map
from KIAS campus map
