Abstract
A problem appearing when the Euler equation is used in the theory of antenna synthesis is considered. Behavior of a solution to this equation at the ends of the synthesis interval contradicts the Meixner conditions, according to which this solution must tend to zero as a square root of the distance to the ends. It is shown that this contradiction arises if we seek solutions in the L 2 space and disappears if an L 2 subspace with limited energy norm is selected as the space of solutions. In this case, the Euler equation arises from a variational minimization problem for a functional involving the norm of current determined in the energy space.
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References
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S. I. Éminov, Radiotekh. Élektron. (Moscow) 38(12), 2160 (1993).
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Translated from Pis’ma v Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 26, No. 14, 2000, pp. 97–102.
Original Russian Text Copyright © 2000 by Éminov.
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Éminov, S.I. On the Euler equation appearing in the synthesis of radiating systems. Tech. Phys. Lett. 26, 637–639 (2000). https://doi.org/10.1134/1.1262939
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DOI: https://doi.org/10.1134/1.1262939