学术报告
Existence Theorems for a Crystal Surface Model
题 目： Existence Theorems for a Crystal Surface Model
报告人：Prof. Xiangsheng Xu (Department of Mathematics and Statistics, Mississippi State University)
摘要: This is a joint work with Jian-Guo Liu of Duke University. We consider the existence assertion for the initial-boundary value problem for the equation 
. This equation arises in the mathematical modeling of the evolution of crystal surfaces. Mathematically, it is a fourth order nonlinear parabolic equation with both singularity and degeneracy. In particular, we have very little a priori control over the exponent term 
. Our investigations reveal that the exponent in the equation can have a singular part in the sense of the Lebesgue Decomposition Theorem and the exponential nonlinearity somehow “cancels” it out. The net result is that we obtain a solution u that satisfies the equation and the initial boundary conditions in the a.e. sense. We will address three issues: 1. how to construct a sequence of approximate solutions to the problem, 2. how to derive a priori estimates for the sequence, and 3. how to justify passing to the limit in the approximating problems.
时间：5月26日（周四）下午4:00-5:00
地点：首都师大北一区文科楼709教室
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