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(1.2) { u(x) = u0(x), u ′(x, 0) = u1(x), in Ω, u′(x,−t) = f0(x,−t), in Ω× (0, τ2), where (u0, u1, f0) are given history and initial data. Here ∆ denotes the Laplacian operator and ∆e denotes the elasticity operator, which is the 3×3 matrix-valued differential operator defined by ∆eu = μ∆u+ (λ+ μ)∇(div u), u = (u1, u2, u3) and μ and λ are the Lamé constants which satisfy the conditions (1.3) μ > 0, λ+ μ ≥ 0. Moreover, μ2 : [τ1, τ2] → R is a bounded function and τ1 < τ2 are two positive constants.

Well-posedness and asymptotic stability for the Lamé system with internal distributed delay