Work

Linear stability of the non-zero equilibrium state for the viscous Burgers equation with time delay

Year: 2025

Type: article

Abstract: In this article, we consider the linear stability of the non-zero equilibrium state for the viscous Burgers equation with a delay effect. The linear stability is analyzed by using the characteristic equation of the corresponding eigenvalue problem. If our equation does not have a delay effect, the characteristic equation is given by a polynomial equation. On the other hand, if our equation has a delay effect, the characteristic equation becomes a transcendental equation, and it is difficult to analyze it. In this situation, we apply the useful known result concerned with the characteristic equation for the ordinary delay differential equations and try to get the sharp stability condition for the viscous Burgers equation with delay. Furthermore, we apply the obtained results to a model of the traffic flow.

Source: Japan Journal of Industrial and Applied Mathematics

DOI: 10.1007/s13160-025-00706-5

Author: Yoshihiro Ueda

Institution: Kobe University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Kobe University, Japan Society for the Promotion of Science