Weak and strong solutions of a nonlinear subsonic flow–structure interaction: Semigroup approach

Abstract

We consider a non-rotational, subsonic flow–structure interaction describing the flow of gas above a flexible plate. A perturbed wave equation describes the flow, and a second-order nonlinear plate equation describes the plate’s displacement. It is shown that the linearization of the model generates a strongly continuous semigroup with respect to the topology generated by “finite energy” considerations. An interesting feature of the problem is that linear perturbed flow–structure interaction is not monotone with respect to the standard norm describing the finite energy space. The main tool used in overcoming this difficulty is the construction of a suitable inner product on the finite energy space which allows the application of ω -maximal monotone operator theory. The obtained result allows us to employ suitable perturbation theory in order to discuss well-posedness of weak and strong solutions corresponding to several classes of nonlinear dynamics including the full flow–structure interaction with von Karman, Berger’s and other semilinear plate equations.