## Lectures

### 2011/11/18

15:00-16:00   Room #052 (Graduate School of Math. Sci. Bldg.)
Hiroshi Isozaki (University of Tsukuba)
Inverse problems for heat equations with discontinuous conductivities
(JAPANESE)
[ Abstract ]
In a bounded domain $\\Omega \\subset {\\bf R}^n$, consider the heat
equation $\\partial_tu = \\nabla(\\gamma(t,x)\\nabla u)$. The heat
conductivity is assumed to be piecewise constant : $\\gamma = k^2$ on
$\\Omaga_1(t) \\subset\\subset \\Omega$, $\\gamma(t,x) = 1$ on
$\\Omega\\setminus\\Omega_1(t)$. In this talk, we present recent results
for the inverse problems of reconstructing $\\gamma(t,x)$ from the
Dirichlet-to-Neumann map :
$u(t)|_{\\partial\\Omega} \\to$\\partial_{\\nu}u|_{\\partial\\Omega}$for a time interval$(0,T)\$. These are the joint works with P.Gaitan, O.Poisson,
S.Siltanen, J.Tamminen.