Stabilization for a degenerate wave equation with drift and potential term with boundary fractional derivative control

Abstract

This paper explores the boundary stabilization of a degenerate wave equation in the non-divergence form, which includes a drift term and a singular potential term. Additionally, we introduce boundary fractional derivative damping at the endpoint where divergence is absent. Using semi-group theory and the multiplier method, we establish polynomial stability, with a decay rate depending upon the order of the fractional derivative.

Keywords

• degenerate wave equation
• singular potentials
• drift
• boundary stabilization
• polynomial decay
• fractional derivative
• non-divergence form