SMS scnews item created by Eduardo Altmann at Mon 17 Jul 2017 0527
Type: Seminar
Distribution: World
Expiry: 14 Aug 2017
Calendar1: 2 Aug 2017 1400-1500
CalLoc1: AGR Carslaw 829
CalTitle1: Boundary layers arising from chemotaxis models tration problem
Auth: ega@78.11.31.131 (egol5583) in SMS-WASM

# Boundary layers arising from chemotaxis models

### Wang

A/Prof Zhi-An Wang (Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong)
Title: Boundary layers arising from chemotaxis models
Abstract: The original well-known Keller-Segel system describing the chemotactic wave propagation remains poorly understood in many aspects due to the logarithmic singularity. As the chemical assumption rate is linear, the singular Keller-Segel model can be converted, via a Cole-Hopf type transformation, into a system of viscous conservation laws without singularity. In this talk, we first consider the dynamics of the transformed Keller-Segel system in a bounded interval with time-dependent Dirichlet boundary conditions. By imposing some conditions on the boundary data, we show that boundary layer profiles are present as chemical diffusion tends to zero and large-time profile of solutions will be determined by the boundary data (i.e. boundary stabilization). We employ the refined (weighted) energy estimates with the effective viscous flux" technique to show the emergence of boundary layer profiles. For asymptotic dynamics of solutions, we develop a new idea by exploring the convexity of an entropy expansion to get the basic $L^1$-estimate, on which our results are built up by the method of energy estimates. Finally we gain the results for the original singular Keller-Segel system by reversing the Cole-Hopf transformation. Numerical simulations are performed to interpret our analytical results and their implications.

Seminars are held at 2:00 pm on Wednesdays in the Access Grid Room ( Carslaw Building, 8th floor, room 829), unless otherwise noted.

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