Conference on
Partial Differential Equations and Applications
August 14-17, 2003

(574) 631-7245
Fax: (574) 631-6579

Tentative Schedule

II. Nonlinear Elliptic and Parabolic Equations and Applications.
Organized by Qing Han and Bei Hu

Confirmed Speakers:

1. X. Chen, Univeristy of Pittsburgh
   Title: "On finite range repulsive systems of finitely many particles."
   
2. Nikolai Chemetov, University of Lisbon
   Title: "On a motion of a perfect fluid through a given domain."
   
3. Gheorghe Craciun, Ohio State
   Title: "Some inverse problems for classical models of electrical activity along dendrites"
   
4. M. Feldman, University of Wisconsin
   Title: "Transonic shocks and free boundary problems"
   
5. Peng Feng, Michigan State
   Title: "Radial symmetry and symmetry breaking for a semilinear elliptic equation modeling MEMS."
   
6. A. Friedman, Ohio State University
   Titles: See below
   
7. J. Guo, National Taiwan Normal University
   Title: "On a two-pooint free boundary problem"
   
8. Yi Li, University of Iowa
   Title: " The Global Dynamics of Isothermal Chemical Systems with Critical Nonlinearity"
   
9. Yuan Lou, Ohio State
   Title: "Competing species near a degenerate limit"
   
10. D. Phillips, Purdue University
    Title: "Analytic Aspects of Transitions in Liquid Crystals"
    
11. Yuxi Zheng, Penn State
    Title: "A global solution to a 2-D Riemann problem"

Minicourse Spearker:

A. Friedman, Ohio State University.

• Lecture 1. Old and new free boundary problems (Aug 14)
  Abstract: I will review some classical free boundary problems, including variational inequalities, the Stefan problem, and the Hele Shaw problem. Next I will describe some free boundary problems for systems of PDEs which arise in models of cancer, and state some recent results on existence theorems, and some open problems.
  
• Lecture 2. Asymptotic behavior for solutions of cancer models (Aug 15)
  Abstract: I will consider the asymptotic behavior of the free boundary for several of the cancer models introduced in the previous lecture. I will also introduce a model of cancer therapy and consider the question how to optimally schedule the drug treatment.
  
• Lecture 3. Symmetry-breaking bifurcations of free boundary problems (Lecture 3 will be held in Session II on Aug 15).
  Abstract: It was proved in recent years, for some free boundary problems for systems of elliptic PDEs, that there exists symmetry-breaking bifurcation branches of solutions. In this talk, I shall describe a unified method for proving such results, based in part on applying the Crandall-Rabinowitz theorem.