Communications in Mathematical Sciences

Volume 21 (2023)

Number 3

Local sensitivity analysis for the Vicsek-type self-organized hydrodynamic model

Pages: 591 – 625

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n3.a1

Authors

Ning Jiang (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Zeng Zhang (School of Science, Wuhan University of Technology, Wuhan, China)

Abstract

We consider the Vicsek-type self-organized hydrodynamic (SOH) model with random inputs. In the absence of random inputs, the SOH model was derived as a macroscopic limit from the Vicsek model. Considering the uncertainty, which is modeled by a random parameter and enters into the SOH model through the initial data, we perform the local sensitivity analysis to study the regularity with respect to the random parameter and the stability of solutions to the random SOH model.

Keywords

self-organized hydrodynamic model, Vicsek model, local sensitivity analysis

2010 Mathematics Subject Classification

35A01, 35Q35, 49K40

Received 26 November 2021

Received revised 20 June 2022

Accepted 27 June 2022

Published 27 February 2023