Geometry effects on the boundary-layer profiles of the Keller-Segel system

Year: 2025

Type: article

Abstract: We consider the boundary-layer problem of a nonlocal semilinear elliptic equation in a bounded smooth domain of all dimensions with the Dirichlet boundary condition, which arises as the stationary problem of the Keller-Segel system with physical boundary conditions describing the boundary-layer formation driven by chemotaxis. Using the Fermi coordinates and delicate analysis with subtle estimates, we rigorously derive the asymptotic expansion of the boundary-layer profile and thickness in terms of the small diffusion rate with coefficients explicitly expressed by the domain geometric properties including mean curvature, volume and surface area. By these expansions, one can explicitly find the joint impact of the mean curvature, surface area and volume of the spatial domain on the boundary-layer steepness and thickness. This seems to be the first result revealing how the boundary-layer profiles depend on the domain geometries for chemotaxis models.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/tran/9528

Authors: Chiun-Chang Lee, Sang-Hyuck Moon, Zhi-An Wang, Wen Yang

Institutions: National Tsing Hua University, Pusan National University, Hong Kong Polytechnic University, University of Macau

Language: English

Topic: Mathematical Biology Tumor Growth

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Ministry of Science and Technology, Taiwan, Universidade de Macau, Ministry of Science and ICT, South Korea, University Research Committee, University of Hong Kong, National Key Research and Development Program of China

OpenAlex ID: W4413964734