Input-output relations for systems described by parabolic equations

Abstract

This paper deals with the boundary value problem for a system described by a fourth-order parabolic equation which has been derived for the vibratory motion of an elastic plate. By defining the bending moment and the stress acting on the boundary as the input, and the displacement and the inclination at the boundary as the output, the direct and inverse input-output relations have been obtained. General parabolic systems with boundary inputs and boundary outputs are dealt with, and the input-output relations are obtained, accompanied with some examples.