Energy decay for nonlinear Kirchhoff-like type wave equation with nonlinear velocity feedback

摘要

1 Introduction We investigate on the global existence and energy decay of solutions to the following Kirchhoff-like type wave equation {u"-divA(u)▽u + |u'|βu' = 0, (t, x) ∈ [0,+∞) × Ω, u = 0, (t, x) ∈ (0,+∞) × Γ, u(0, x) = u0(x), u'(0, x) = u1(x), x∈ Ω, (1) where' = d/dt , Ω is a bounded domain in Rn with smooth boundary Γ.