Lecture Room B, 4th Floor, The 3rd General Building, NTHU
(清華大學綜合三館 4樓B演講室)
Spreading Speeds of Noncompact Evolution Equations in Spatially Periodic Media
Weiwei Ding (South China Normal University)
Abstract:
In this seminar, I will discuss the existence of spreading speeds for noncompact evolution equations in spatially periodic media. Firstly, I will introduce an abstract framework on the existence of spreading speeds for general spatially periodic noncompact operators, under the assumption that the linearized operators admit a principal eigenvalue. Then I will show the existence of principal eigenvalues for a class of generalized convolution operators on the circle. Finally, I will apply the above two results to an integro-difference equation and a non-local diffusion equation with KPP nonlinearities, and further discuss what kind of dispersal kernels can guarantee the existence of spreading speeds in the two equations. This talk is based on a joint work with Xing Liang (SIMA, 2015).