Closed-form expression for a generalized solution in Wp1 of a mixed problem describing radially symmetric vibrations of a three-dimensional ball

For any p >= 1 and any time interval [0, T], we derive a closed-form expression for a generalized solution in W (p) (1) of a mixed problem describing the radially symmetric vibrations of a three-dimensional ball with arbitrary initial conditions and an arbitrary boundary control on the ball surface by a boundary condition of the first kind.