Well-posedness of inverse problems for systems with time dependent parameters
Harvey Thomas Banks, Michael Pedersen · NCSU Libraries Repository (North Carolina State University Libraries) · 2008
In this paper we investigate the abstract hyperbolic model with time dependent stiffness and damping given byare Hilbert spaces with continuous and dense injections, where H is identified with its dual and •, • denotes the associated duality product.We show under reasonable assumptions on the time-dependent sesquilinear forms a(t; •, •) : V × V → C and d(t; •, •) : V D × V D → C that this model allows a unique solution and that the solution depends continuously on the data of the problem.We also consider well-posedness as well as finite element type approximations in associated inverse problems.The problem above is a weak formulation that includes models in abstract differential operator form that include plate, beam and shell equations with several important kinds of damping.