|
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
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
Linking options:
https://www.mathnet.ru/eng/znsl5856 https://www.mathnet.ru/eng/znsl/v210/p30
|
Statistics & downloads: |
Abstract page: | 153 | Full-text PDF : | 53 |
|