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@ (egol5583) in SMS-WASM

Applied Maths Seminar

Boundary layers arising from chemotaxis models


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.

See the Applied Maths Seminar Webpage

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