Eigenvalue Problems and Applications in the Population Dynamics with Nonlocal Dispersal

This talk concerns the population dynamics modeled by the KPP-type equations with nonlocal dispersal operators. It is well known that a population's persistence is uniquely determined by the sign of the generalized principal eigenvalue of the linearized KPP-type equation at the zero solution. A better understanding of the eigenvalue problem is of both theoretical and practical importance.

In this talk, I will discuss the spectral theory for nonlocal dispersal operators with time-periodic indefinite weight functions subject to Dirichlet type, Neumann type, and spatial periodic type boundary conditions. I first obtain necessary and sufficient conditions for the existence of a unique positive principal spectrum point for such operators and then investigate the upper bounds of principal spectrum points and sufficient conditions for the principal spectrum points to be principal eigenvalues. Finally, I discuss the applications of nonlinear mathematical models from biology.

Event Topic

Stochastic & Multiscale Modeling and Computation