|Existence theorems for a class of fourth-order nonlinear parabolic equations|
|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|
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 A well-known difficulty in the study of these types of equations is that the maximum principle is no longer valid.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.
Real and functional analysis. Some knowledge of classical regularity theory for linear elliptic and parabolic equations is also helpful.
D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin, 1983.