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On the Uniqueness of the Recovery of Parameters of the Maxwell System from Dynamical Boundary Data

Authors:

Institution:

(1) St.Petersburg Department of the Steklov Mathematical Institute, Russia;(2) Department of Mathematics and Statistics, Wichita State University, USA

Abstract:

The paper deals with the problem of recovering the parameters (functions) $\varepsilon$ and $\mu$ of the Maxwell dynamical system

$\varepsilon E_t = {\text{rot}}\,H,\quad \mu H_t = - {\text{rot}}\,E\quad in\quad \Omega \times \left( {0,T} \right);$

$E\left| {_{t = 0} = 0,\quad H} \right|_{t = 0} = 0\quad in\quad \Omega ;$

$E_{\tan } = f\quad on\quad \partial \Omega \times \left {0,T} \right]$

(tan is the tangent component; $E = E^f \left( {x,t} \right),H = H^f \left( {x,t} \right)$ is a solution) by the response operator $R^T :f \to \nu \times H^f \left| {_{\partial \Omega \times \left {0,T} \right]} } \right.$ ( $\nu$ is the normal). The parameters determine the velocity $c = \left( {\varepsilon \mu } \right)^{ - \frac{1}{2}}$ , the c-metric $ds^2 = c^{ - 2} \left| {dx} \right|^2$ , and the time $T_* = \mathop {\max }\limits_\Omega {\text{dist}}_c \left( { \cdot ,\partial \Omega } \right)$ . It is shown that for any fixed $$T > T$$

, the operator $R^{2T}$ determines $\varepsilon$ and $\mu$ in $\Omega$ uniquely. Bibliography: 15 titles.

Keywords:

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