Control and stabilization results for strongly coupled degenerate/singular hyperbolic systems
Year: 2025
Type: article
Abstract: In this paper, we consider a system of two degenerate and singular wave equations coupled through velocities, where only one of the equations is controlled or damped. Under some technical assumptions on the coefficients of the system, we prove new controllability and stability results. First, we derive the explicit time for the indirect controllability of the corresponding control problem. Second, we prove that the total energy of the associated stabilization problem is exponentially decaying to zero, providing an explicit formula for the decay rate. The proofs of our results are mainly based on careful energy estimates and suitable Hardy-Poincaré type inequalities.
DOI: 10.3934/mcrf.2025057
Authors: Mohamed Azzaoui, Alhabib Moumni, Jawad Salhi, Mouhcine Tilioua
Institution: Université Moulay Ismail de Meknes
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7088323383