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Flow-plate interactions: Well-posedness and long-time behavior

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https://ir.library.oregonstate.edu/concern/articles/1831cm75q

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Abstract
  • We consider flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are treated with Neumann type flow conditions, and a novel treatment of the so called Kutta-Joukowsky flow conditions are given in the subsonic case. The goal of the paper is threefold: (i) to provide an accurate review of recent results on existence, uniqueness, and stability of weak solutions, (ii) to present a construction of finite dimensional, attracting sets corresponding to the structural dynamics and discuss convergence of trajectories, and (iii) to state several open questions associated with the topic. This second task is based on a decoupling technique which reduces the analysis of the full flow-structure system to a PDE system with delay.
  • Keywords: Well-posedness, Nonlinear semigroups, Flow-structure interaction, PDE with delay, Global attractors, Nonlinear plate
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  • Chueshov, I., Lasiecka, I., & Webster, J. (2014). Flow-plate interactions: Well-posedness and long-time behavior. Discrete and Continuous Dynamical Systems - Series S, 7(5), 925-965. doi:10.3934/dcdss.2014.7.925
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  • 7
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  • 5
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  • The research conducted by the second author was supported by the grants NSF-DMS-0606682 and AFOSR-FA99550-9-1-0459. The second and third authors are grateful to Prof. A.V. Balakrishnan for a longtime sharing of his pioneering results in the field of continuum aeroelasticity. Additionally, the authors are grateful to Prof. E. Dowell for very constructive and informative ongoing discussion regarding flow-structure interaction models and configurations of recent interest.
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