Geodesic
A continuation problem for electrodynamic equations
Eurasian journal of mathematical and computer applications, Tome 7 (2019) no. 4, pp. 100-114.

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We consider the problem of continuation of a solution of electrodynamic equations from the boundary of the half-space $\mathbb{R}_+^3=\{x\in\mathbb{R}^3\mid x_3>0\}$ inside. The main result is a unique local solvability and uniqueness theorem in the class of functions that are analytic with respect to space variables.
Keywords: Maxwell equations, Cauchy problem, uniqueness, solvability. 
@article{EJMCA_2019_7_4_a6,
     author = {V. G. Romanov},
     title = {A continuation problem for electrodynamic equations},
     journal = {Eurasian journal of mathematical and computer applications},
     pages = {100--114},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJMCA_2019_7_4_a6/}
}
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V. G. Romanov. A continuation problem for electrodynamic equations. Eurasian journal of mathematical and computer applications, Tome 7 (2019) no. 4, pp. 100-114. http://geodesic.mathdoc.fr/item/EJMCA_2019_7_4_a6/