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In this paper we study the stability of two different problems. The first oneis a one-dimensional degenerate wave equation with degenerate damping,incorporating a drift term and a leading operator in non-divergence form. Inthe second problem we consider a system that couples degenerate andnon-degenerate wave equations, connected through transmission, and subject to asingle dissipation law at the boundary of the non-degenerate equation. In bothscenarios, we derive exponential stability results.

Stability for degenerate wave equations with drift under simultaneous degenerate damping