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Generation of bounded semigroups in nonlinear subsonic flow–structure interactions with boundary dissipation
Author(s) -
Lasiecka Irena,
Webster Justin
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1518
Subject(s) - semigroup , mathematics , nonlinear system , bounded function , flow (mathematics) , dissipation , inertia , mathematical analysis , boundary (topology) , boundary value problem , geometry , classical mechanics , physics , quantum mechanics , thermodynamics
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 S γ ( t ) converge to S 0 ( 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.