报告人简介：Yong-Jung Kim obtained his Ph.D. in mathematics from University of Wisconsin at Madison in 1999. His thesis title was `Scaling invariance in hyperbolic conservation laws'. He had his post-doctoral positions at Universities of Minnesota, Toronto, and California-Riverside. He is currently a full professor at KAIST (Korean Advanced Institute of Science and Technology). His current research interests are focused on diffusion theory, population dynamics, and mathematical modeling.
In this talk we consider a bistable nonlinearity with a jump discontinuity at a stable steady state. To handle the discontinuous nonlinearity, we define the weak solution in terms of set-valued integration. The existence, uniqueness, and the comparison property still hold. One of new feature of the problem is finite time extinction and existence of traveling waves with a free boundary.
主持人： 潘兴斌 教授