Polynomial decay of the energy of solutions of coupled wave equations with locally boundary fractional dissipation

Abstract

Abstract In this paper, we investigate a system of coupled wave equations featuring boundary fractional damping applied to a portion of the domain. We first establish the well-posedness of the system, proving the existence and uniqueness of solutions through semi-group theory. While the system does not exhibit exponential stability, we demonstrate its strong stability. Furthermore, leveraging Arendt and Batty’s general criteria and certain geometric conditions, we prove a polynomial rate of energy decay for the solutions.

Keywords

• Wave equations
• Fractional derivatives
• C 0 $\mathcal{C}_{0}$ semi-group
• General decay