[PAST EVENT] Mathematics Colloquium: Xing Liang (University of Science and Technology of China, China)
November 17, 2014
10am - 11am
Abstract:The main aim of this paper is to understand what kind of diffusion mechanism can guarantee the existence of the spreading speed for an evolution system in the periodic media. The following three parts of works are included in this paper: First, the uniform irreducibility of Radon measures on the circle is defined, and it is proved that the generalized convolution operator generated by a uniformly irreducible and nonnegative measure has the principal eigenvalue. Next, an abstract framework of the spreading speeds for general spatially periodic noncompact systems is established, the variational formula of the spreading speeds is given under the hypothesis that the principal eigenvalues of the linearized systems exist. Finally, based on the above two preparations, it is shown that the uniform irreducibility of the diffusion can guarantee the existence of the spreading speed in the periodic media through investigating the integro-dfference system.