著者

Gaitan P. Isozaki H. Poisson O. Siltanen S. Tamminen J. P.

出版者

Society for Industrial and Applied Mathematics

雑誌

SIAM journal on mathematical analysis (ISSN:00361410)

巻号頁・発行日

vol.45, no.3, pp.1675-1690, 2013-05

被引用文献数

5

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We consider an inverse boundary value problem for the heat equation on the interval $(0,1)$, where the heat conductivity $\gamma(t,x)$ is piecewise constant and the point of discontinuity depends on time: $\gamma(t,x) = k^2 \ (0 < x < s(t))$, $\gamma(t,x) = 1\ (s(t) < x < 1)$. First, we show that $k$ and $s(t)$ on the time interval $[0,T]$ are determined from a partial Dirichlet-to-Neumann map: $u(t,1) \to \partial_xu(t,1), \ 0 < t < T$, $u(t,x)$ being the solution to the heat equation such that $u(t,0)=0$, independently of the initial data $u(0,x)$. Second, we show that another partial Dirichlet-to-Neumann map: $u(t,0) \to \partial_xu(t,1), \ 0 < t < T$, $u(t,x)$ being the solution to the heat equation such that $u(t,1)=0$, restricts the pair $(k,s(t))$ to, at most, two cases on the time interval $[0,T]$, independently of the initial data $u(0,x)$.