Program
Existence theorems for a class of fourth-order nonlinear parabolic equations
Student No.:50
Time:Tue/Thu 10:10-12:00, 2016-05-05~ 2016-05-26
Instructor:Xiangsheng Xu  [Mississippi State University]
Place:Conference Room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2016-5-5
Ending Date:2016-5-26
 

 

Description:

 

 

Fourth-order nonlinear parabolic equations arise in a variety of physical applications. The most famous examples are quantum semiconductor models, thin film equations, continuous models for epitaxial growth of crystal surfaces, and so on. A well-known difficulty in the study of these types of equations is that the maximum principle is no longer valid. In fact, the heat kernel for the bi-harmonic heat equation changes signs. Thus we must rely on the nonlinear structure of our equations to obtain non-negative solutions. In this lecture series, we will study the most recent techniques on how to do that. Another issue is how to prescribe physically-realistic boundary conditions for fourth-order equations. All these problems have attracted a lot of attention, and they are the hot topic of current mathematical research.

 

 

 

Prerequisite:

 

 

Real and functional analysis. Some knowledge of classical regularity theory for linear elliptic and parabolic equations is also helpful.

 

 

 

Reference:

 

 

D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin, 1983.