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Zapiski Nauchnykh Seminarov POMI, 2000, Volume 264, Pages 311–320
(Mi znsl1184)
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On boundary value problems for a version of Maxwell equations
Sh. Sakhaev Saint-Petersburg State University
Abstract:
Boundary value problem for the system of equations
$$
\operatorname{rot}\vec H-\sigma\vec E=0, \quad \operatorname{rot}\vec E+\mu\vec H=0,
$$
(where $\sigma$ and $\mu$ are positive constants) in a domain $\Omega\Subset R^3$ are considered. Boundary conditions are
$$
H_n\big|_{\partial\Omega}=\varphi(x)\big|_{\partial\Omega},\ \ E_n\big|_{\partial\Omega}=f(x)\big|_{\partial\Omega}.
$$
The correcntess of the problem is proved if $\partial\Omega$ is smooth. The potential theory is used to get this result.
Received: 10.01.2000
Citation:
Sh. Sakhaev, “On boundary value problems for a version of Maxwell equations”, Mathematical problems in the theory of wave propagation. Part 29, Zap. Nauchn. Sem. POMI, 264, POMI, St. Petersburg, 2000, 311–320; J. Math. Sci. (New York), 111:5 (2002), 3806–3811
Linking options:
https://www.mathnet.ru/eng/znsl1184 https://www.mathnet.ru/eng/znsl/v264/p311
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