Generation of bounded semigroups in nonlinear subsonic flow-structure interactions with boundary dissipation


We consider a 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. We consider the model that accounts for rotational inertia in the plate, parametrized by γ ≥ 0. It is known that the presence of γ > 0 has strong effect on regularity properties of the plate, which then allows one to establish well-posedness of finite energy solutions for the entire structure. In this paper, it is shown that semigroup well-posedness of the model is not only preserved for all γ ≥ 0 but that the corresponding nonlinear semigroups Sγ(t) converge to S0(t) when γ → 0. The above result holds also in the presence of nonlinear boundary damping. In addition, we provide a discussion of the regularity of strong solutions. Copyright © 2011 John Wiley & Sons, Ltd.

Publication Title

Mathematical Methods in the Applied Sciences