Geodesic
The uniqueness of the Cauchy problem solution for the Maxwell equations, when the initial data are fixed on a time-like surface
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 23, Tome 210 (1994), pp. 30-37 
V. M. Babich. The uniqueness of the Cauchy problem solution for the Maxwell equations, when the initial data are fixed on a time-like surface. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 23, Tome 210 (1994), pp. 30-37. http://geodesic.mathdoc.fr/item/ZNSL_1994_210_a2/
@article{ZNSL_1994_210_a2,
     author = {V. M. Babich},
     title = {The uniqueness of the {Cauchy} problem solution for the {Maxwell} equations, when the initial data are fixed on a~time-like surface},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {30--37},
     year = {1994},
     volume = {210},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_210_a2/}
}
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The uniqueness theorem for the Canchy problem $$ \begin{gathered} \frac\mu c\,\frac{\partial\overrightarrow H}{\partial t}=-\operatorname{rot}\overrightarrow E,\ \ \operatorname{div}\mu\overrightarrow H=0,\quad \frac\varepsilon c\,\frac{\partial\overrightarrow E}{\partial t}=-\operatorname{rot}\overrightarrow H,\ \ \operatorname{div}\varepsilon\overrightarrow E=0, \quad\varepsilon>0,\ \ \mu>0,\\ \overrightarrow H|_\Sigma=0,\quad\overrightarrow E|_\Sigma=0,\qquad\Sigma=\Gamma\times[0\le t\le2T],\quad0<T<+\infty, \end{gathered} $$ ($\varepsilon=\varepsilon(x)$, $\mu=\mu(x)$ are analytical functions, $\Gamma\subset\mathbb R^3$ – an analytical surface) is proved. Bibliography: 5 titles.