Stability for a nonlinear hyperbolic equation with time-dependent coefficients and boundary damping.

In this paper, we prove a stability result for a nonlinear wave equation, defined in a bounded domain of R N , N ≥ 2 , with time-dependent coefficients. The smooth boundary of Ω is Γ = Γ 0 ∪ Γ 1 such that Σ = Γ ¯ 0 ∩ Γ ¯ 1 ≠ ∅ . On Γ 0 we consider the homogeneous Dirichlet boundary condition and on Γ 1 we consider the Neumann boundary condition with damping term. The presence of time-dependent coefficients and, moreover, of the singularities generated by the condition Σ ≠ ∅ brings some technical difficulties. The tools are the combination of appropriate functional with the techniques due to Bey, Loheac, and Moussaoui [2] and new technical arguments. [ABSTRACT FROM AUTHOR]