Recovering two Lame' kernels in a viscoelastic system

Let ${\cal B}$ be a viscoelastic body with a (smooth) bounded open reference set $\Omega$ in $R^3$, with the equation of motion being described by the Lame' coefficients $\lambda_0$ and $\mu_0$ and the related viscoelastic coefficients $\lambda_1$ and $\mu_1$. The latter are assumed to be factorized with the same temporal part, i.e. $\lambda_1(t,x)=k(t)p(x)$ and $\mu_1(t,x)=k(t)q(x)$. Furthermore, it is assumed that the spatial parts $p$ and $q$ of $\lambda_1$ and $\mu_1$ are unknown and the three additional measurements $\sum_{j=1}^3\sigma_{i,j}^0(t,x){\bf n}_j(x) = g_i(t,x)$, $i=1,2,3$, are available on $(0,T)\times \partial \Omega$ for some (sufficiently large) subset $\Gamma\subset \partial \Omega$.