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NCTS Seminar on Mathematical Biology
14:10 - 16:00, October 20, 2017 (Friday)
Lecture Room B, 4th Floor, The 3rd General Building, NTHU
(清華大學綜合三館四樓 B演講室)
Existence and Instability of Traveling Pulses of Keller-Segel System with Nonlinear Chemical Gradients and Small Diffusions
Yu-Shuo Chen (Tamkang University)


In this study, we consider a generalized model of 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 profiles 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 instability of these pulses by the spectral analysis of the linearized operators.


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