Nonlinear PDE seminars, KIAS

Organizers:

• Ki-Ahm Lee (Seoul National University, KIAS)

  E-mail: kiahm(at)snu.ac.kr
  
  

• Hyunsuk Kang (KIAS)

  Managing Organizer
  E-mail: h.kang(at)kias.re.kr

Fall, 2013

• On the uniqueness of quadrature surfaces

  Michiaki Onodera (Kyushu University)

  Date: 2013.10.04.
  Venue: Room 1424 at KIAS

  Abstract:

  A new geometric flow describing the motion of a closed surface is introduced. We characterize a continuous family of quadrature surfaces by the geometric flow. This characterization reduces the uniqueness of quadrature surfaces to the unique solvability of the geometric flow. In fact, by spectral analysis, we prove the uniqueness under the geometric condition that each surface has positive mean curvature. It should be emphasized that the relation between the geometric flow and quadrature surfaces is an analog of that of the Hele-Shaw flow and quadrature domains.
  
  
  

• Keller-Segel models coupled to fluid equations

  Kyungkeun Kang (Yonsei University)

  Date: 2013.09.27.
  Venue: Room 1423 at KIAS

  Abstract:

  We consider a mathematical model for dynamics of oxygen diffusion and consumption, aerotaxis and viscous incompressible fluids. We discuss local and global existence of regular solutions together with temporal decay estimates of global solutions.
  
  
  

• On the Degenerate Keller-Segel system

  Yoshie Sugiyama (Kyushu University)

  Date: 2013.09.27.
  Venue: Room 1423 at KIAS

  Abstract:

  We consider the system of the Keller-Segel equations with a degenerate type and introduce recent research developments from a view point of partial differential equations. Firstly, we shall bring our result into a focus on the critical exponent which divides the situation between the global existence and finite time blow-up. In particular, the asymptotics of solutions in an infinity time with the optimal convergence rate will be clarified. The extinction phenomenon by which we mean that the solution vanishes on a whole space domain will be also discussed for the system of singular type. In both cases of degenerate and singular type, it should be noticed that the mass conservation law plays an important role. Among these topics, we shall further treat the asymptotic profile of a solution, the $\epsilon$ regularity theorem, the finite speed of propagation, and measure valued solutions.