Work

Time-delayed generalized Korteweg–de Vries-Burgers equation: Well-posedness and exponential decay

Year: 2025

Type: article

Abstract: This study explores the generalized Korteweg-de Vries-Burgers equation incorporating delay feedback and a damping term. Using semigroup arguments and Lyapunov functional techniques, we establish the existence of a global solution when the exponent of the nonlinear term satisfies some growth conditions. Furthermore, we prove exponential stability estimates under suitable assumptions: first in the case of a positive damping coefficient, then within a more comprehensive framework, accommodating sign changes in both coefficients, i.e. for the damping and the delay feedback. In both cases, we adopt refined conditions on the delay feedback’s coefficient, extending and enhancing existing results in the literature. In particular, our conditions are independent of the time delay size.

Source: Nonlinear Analysis Real World Applications

DOI: 10.1016/j.nonrwa.2025.104519

Authors: Ibtissam Issa, Cristina Pignotti

Institution: University of L'Aquila

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: $3,780

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni