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We prove existence and uniform stability of strong solutions to aquasilinear wave equation with a locally distributed nonlinear dissipation with source term of power nonlinearity ofthe type u″−M(∫Ω|∇u|2dx)Δu+a(x)g(u′)+f(u)=0, in Ω×]0,+∞[, u=0, on Γ×]0,+∞[,u(x,0)=u0(x),u′(x,0)=u1(x), in Ω

On the global solvability of solutions to a quasilinear wave equation with localized damping and source terms