Existence and Instability of Traveling Pulses of Generalized Keller-Segel Equations with Nonlinear Chemical Gradients and Small Diffusions
陳俞碩先生國立中央大學數學系 下午 4:00–5:00 鴻經館 107 室Abstract：
In this paper, we consider a generalized model of 2×2 Keller-Segel system with nonlinear chemical gradient and small cell diffusion. The existence of the traveling pulses for such equations is established by the methods of geometric singular perturbation (GSP in short) and trapping regions from dynamical systems theory. By the technique of GSP, we show that the necessary condition for the existence of traveling pulses is that their limiting proles with vanishing diffusion can only consist of the slow flows on the critical manifold of the corresponding algebraic-differential system. We also consider the linear stability of these pulses by the spectral analysis
of the linearized operators.