Applied Mathematics & Optimization

, Volume 73, Issue 3, pp 475–500 | Cite as

Nonlinear Elastic Plate in a Flow of Gas: Recent Results and Conjectures

  • Igor Chueshov
  • Earl H. Dowell
  • Irena Lasiecka
  • Justin T. Webster


We give a survey of recent results on 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 considered. The focus of the discussion here is on the interesting mathematical aspects of physical phenomena occurring in aeroelasticity, such as flutter and divergence. This leads to a partial differential equation treatment of issues such as well-posedness of finite energy solutions, and long-time (asymptotic) behavior. The latter includes theory of asymptotic stability, convergence to equilibria, and to global attracting sets. We complete the discussion with several well known observations and conjectures based on experimental/numerical studies.


Flow–structure interaction Nonlinear plate Flutter Well-posedness Long-time dynamics Global attractors 



The authors would like to dedicate this work to Professor A.V. Balakrishnan, whose pioneering and insightful work on flutter brought together engineers and mathematicians alike. E.H. Dowell was partially supported by the National Science Foundation with grant NSF-ECCS-1307778. I. Lasiecka was partially supported by the National Science Foundation with grant NSF-DMS-0606682 and the United States Air Force Office of Scientific Research with grant AFOSR-FA99550-9-1-0459. J.T. Webster was partially supported by National Science Foundation with Grant NSF-DMS-1504697.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Igor Chueshov
    • 1
  • Earl H. Dowell
    • 2
  • Irena Lasiecka
    • 3
    • 4
  • Justin T. Webster
    • 5
  1. 1.Kharkov National UniversityKharkovUkraine
  2. 2.Duke UniversityDurhamUSA
  3. 3.University of MemphisMemphisUSA
  4. 4.IBS, Polish Academy of SciencesWarsawPoland
  5. 5.College of CharlestonCharlestonUSA

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