An Inverse Problem for the Dynamical Lame System with Two Sets of Local Boundary Data

From the energy integrals methods [5], it is known that for any initial data u0 ∈ H(1)(), u1 ∈ H(0)() and the lateral Dirichlet data g ∈ C([−T, T ]; H(1)(∂) there is a unique (weak) solution u(; ρ, λ, µ; (u0, u1, g)) to the system of Eq. (7.1) such that

u = u0, ∂t u = u1 on × {0} (7.2)

and

u = g on ∂ × (−T, T ). (7.3)

We will use the following.