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Zapiski Nauchnykh Seminarov POMI, 1994, Volume 210, Pages 30–37 (Mi znsl5856)  

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

St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences
Abstract: 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.
Received: 22.07.1993
English version:
Journal of Mathematical Sciences, 1997, Volume 83, Issue 2, Pages 180–184
DOI: https://doi.org/10.1007/BF02405810
Bibliographic databases:
Document Type: Article
UDC: 517.945.7
Language: Russian
Citation: 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”, Mathematical problems in the theory of wave propagation. Part 23, Zap. Nauchn. Sem. POMI, 210, Nauka, St. Petersburg, 1994, 30–37; J. Math. Sci., 83:2 (1997), 180–184
Citation in format AMSBIB
\Bibitem{Bab94}
\by V.~M.~Babich
\paper The uniqueness of the Cauchy problem solution for the Maxwell equations, when the initial data are fixed on a~time-like surface
\inbook Mathematical problems in the theory of wave propagation. Part~23
\serial Zap. Nauchn. Sem. POMI
\yr 1994
\vol 210
\pages 30--37
\publ Nauka
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5856}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1334741}
\zmath{https://zbmath.org/?q=an:0870.35103}
\transl
\jour J. Math. Sci.
\yr 1997
\vol 83
\issue 2
\pages 180--184
\crossref{https://doi.org/10.1007/BF02405810}
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