报告题目：On Traveling Fronts of Reaction-Diffusion Equations in Spatially Periodic Media 

报告人：王智诚教授  兰州大学

时间：2023年6月17日（周六）上午9: 00-10: 00

腾讯会议：938-928-875 密码：230617

摘要：This talk is concerned with traveling fronts of spatially periodic reaction-diffusion equations with combustion nonlinearity in $\mathbb{R}^N$. It is known that for any given propagation direction $e\in \mathbb{S}^{N-1}$, the equation admits a pulsating front connecting two equilibria $0$ and $1$. We firstly give exact asymptotic behaviors of the pulsating front and its derivatives at infinity, and establish uniform decay estimates of the pulsating fronts at infinity on the propagation direction $e\in \mathbb{S}^{N-1}$. Following the uniform estimates, we then show continuous Fr\'echet differentiability of the pulsating fronts with respect to the propagation direction. Lastly, using the differentiability, we establish  the existence, uniqueness and stability of curved fronts with V-shape in $\mathbb{R}^2$ by constructing suitable super- and subsolutions.