Prof. Chiun-Chang Lee ( Institute of Computational and Modeling Science , National Tsing Hua University)
Title
Asymptotics of Stationary Solutions to Keller-Segel Systems Arising in Chemotaxis
Abstract
In this talk, we introduce the stationary problem of the Keller-Segel system with Dirichlet boundary conditions, a model related to mathematical biology that describes boundary-layer formation driven by chemotaxis. We addresses a fundamental question: How does the geometry of a spatial domain influence the biological pattern formation near its boundary? Using the Fermi coordinates and asymptotic analysis, we establish a rigorous asymptotic expansion for the unique solution in the limit of the small diffusion rate. This result represents the first instance where the dependency of boundary-layer profiles in chemotaxis models on detailed domain geometry. This is a joint work with Sang-Hyuck Moon, Zhian Wang and Wen Yang.
