  Let $\Omega\subset\R^n$, $n\ge 3$, be a smooth bounded domain and consider a
coupled system in $\Omega$ consisting of a conductivity equation $\nabla \cdot
\gamma(x) \nabla u(t,x)=0$ and an anisotropic heat equation
$\kappa^{-1}(x)\partial_t\psi(t,x)=\nabla\cdot (A(x)\nabla
\psi(t,x))+(\gamma\nabla u(t,x))\cdot \nabla u(t,x), \quad t\ge 0$. It is shown
that the coefficients $\gamma$, $\kappa$ and $A=(a_{jk})$ are uniquely
determined from the knowledge of the boundary map $u|_{\partial\Omega}\mapsto
\nu\cdot A\nabla \psi|_{\partial\Omega}$, where $\nu$ is the unit outer normal
to $\partial\Omega$. The coupled system models the following physical
phenomenon. Given a fixed voltage distribution, maintained on the boundary
$\partial\Omega$, an electric current distribution appears inside $\Omega$. The
current in turn acts as a source of heat inside $\Omega$, and the heat flows
out of the body through the boundary. The boundary measurements above then
correspond to the map taking a voltage distribution on the boundary to the
resulting heat flow through the boundary. The presented mathematical results
suggest a new hybrid diffuse imaging modality combining electrical prospecting
and heat transfer-based probing.
