Well Posedness for a Class of Flexible Structure in Hِlder Spaces

During the last few decades, the use of flexible structural systems has steadily increased importance. The study of a flexible aerospace structure is a problem of dynamical system theory governed by partial differential equations. We consider here the problem of characterize well posedness, for a mathematical model of a flexible space structure like a thin uniform rectangular panel. For example, a solar cell array or a spacecraft with flexible attachments. This problem is motivated by both engineering and mathematical considerations. Such mechanical system was mathematically introduced in 1 and consists of a short rigid hub, connected to a flexible panel of length l. Control torque Q t is applied to the hub. The panel is made of viscoelastic material with internal Voigt-type damping with coefficient μ, that is, an ideal dashpot damping which is directly proportional to the first derivative of the longitudinal displacement, and opposing the direction of motion. The equation of motion of the panel is given by