Problem of radially symmetric vibrations of a three-dimensional ball and its optimizationстатья
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Дата последнего поиска статьи во внешних источниках: 17 апреля 2018 г.
Аннотация:We consider radially symmetric vibrations of a
threedimensional ball. The main goal of this paper is
to obtain an explicit analytical expression for the opti
mal boundary control of the vibrations that drives the
ball from an arbitrary prescribed initial state to an arbi
trary prescribed terminal state. The control is pro
duced by a displacement on the ball surface. The opti
mal boundary control is constructed using an explicit
analytical expression for the weak solution (from the
class with p ≥ 1) of the mixed problem in a ball of
radius R for the wave equation
(1)