Well-posedness of inverse problems for systems with time dependent parameters

Abstract EN

In this paper we investigate the abstract hyperbolic model with time dependent stiffness and damping given by h ¨ u(t);yiV;V +d(t; ˙ u(t);y)+a(t;u(t);y) = h f (t);yiV;V where V VD H V D V are Hilbert spaces with continuous and dense injections, where H is identified with its dual and h; i denotes the associated duality product.

We show under reasonable assumptions on the time-dependent sesquilinear forms a(t; ; ) : V V !C and d(t; ; ) :VDVD !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.