Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determining electrical and heat transfer parameters using coupled
  boundary measurements   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.

37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys