Ricerc@Sapienza

We consider an anisotropic hyperbolic equation with memory term: ?t2u(x,t)=?i,j=1n?i(aij(x)?ju)+?0t?|?|?2b?(x,t,?)?x?u(x,?)d?+R(x,t)f(x) for $x \in \Omega$ and $t\in (0, T)$ , which is a simplified model equation for viscoelasticity. The main result is a both-sided Lipschitz stability estimate for an inverse source problem of determining a spatial varying factor $f(x)$ of the force term $R(x, t)\,f(x)$ . The proof is based on a Carleman estimate and due to the anisotropy, the existing transformation technique does not work and we introduce a new transformation of u in order to treat the integral terms.