Well posedness for damped second order systems with unbounded input operators (Q1343202)

A second order in time system is considered, such as those arising in structures with piezoelectric actuators and sensors. It is shown that these systems are most naturally formulated as abstract second order systems with an unbounded nonhomogeneous term. The paper establishes existence, uniqueness and the continuous dependence of solutions in both a weak and a variational setting. A semigroup formulation is used and the conditions under which the variational and semigroup solutions are the same are discussed.