The uniqueness of the Cauchy problem solution for the Maxwell equations, when the initial data are fixed on a~time-like surface

V. M. Babich

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 23, Tome 210 (1994), pp. 30-37

Résumé

The uniqueness theorem for the Canchy problem $$ \begin{gathered} \frac\mu c\,\frac{\partial\overrightarrow H}{\partial t}=-\operatorname{rot}\overrightarrow E,\ \ \operatorname{div}\mu\overrightarrow H=0,\quad \frac\varepsilon c\,\frac{\partial\overrightarrow E}{\partial t}=-\operatorname{rot}\overrightarrow H,\ \ \operatorname{div}\varepsilon\overrightarrow E=0, \quad\varepsilon>0,\ \ \mu>0,\\ \overrightarrow H|_\Sigma=0,\quad\overrightarrow E|_\Sigma=0,\qquad\Sigma=\Gamma\times[0\le t\le2T],\quad0+\infty, \end{gathered} $$ ($\varepsilon=\varepsilon(x)$, $\mu=\mu(x)$ are analytical functions, $\Gamma\subset\mathbb R^3$ – an analytical surface) is proved. Bibliography: 5 titles.