In this talk, we discuss the problem of optimal control for chemotaxis governed by the parabolic-elliptic Patlak-Keller-Segel (PKS) system via flow advection. The main idea is to utilize flow advection for enhancing diffusion to control the nonlinear behavior of the system. The objective is to determine an optimal strategy for adjusting flow strength for advection so that the local in-time blow-up of the solution can be suppressed. Rigorous proof of the existence of an optimal solution and derivation of first-order optimality conditions for solving such a solution are presented. Numerical experiments based on 2D cellular flows in a rectangular domain are conducted to demonstrate our ideas and designs.
Optimal Control for Suppression of Singularity in Chemotaxis via Flow Advection
Weiwei Hu, University of GeorgiaAuthors: Weiwei Hu
2023 AWM Research Symposium
Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]