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

Publication ,  Journal Article
Chueshov, I; Dowell, EH; Lasiecka, I; Webster, JT
Published in: Applied Mathematics and Optimization
June 1, 2016

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.

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Published In

Applied Mathematics and Optimization

DOI

EISSN

1432-0606

ISSN

0095-4616

Publication Date

June 1, 2016

Volume

73

Issue

3

Start / End Page

475 / 500

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

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Chueshov, I., Dowell, E. H., Lasiecka, I., & Webster, J. T. (2016). Nonlinear Elastic Plate in a Flow of Gas: Recent Results and Conjectures. Applied Mathematics and Optimization, 73(3), 475–500. https://doi.org/10.1007/s00245-016-9349-1
Chueshov, I., E. H. Dowell, I. Lasiecka, and J. T. Webster. “Nonlinear Elastic Plate in a Flow of Gas: Recent Results and Conjectures.” Applied Mathematics and Optimization 73, no. 3 (June 1, 2016): 475–500. https://doi.org/10.1007/s00245-016-9349-1.
Chueshov I, Dowell EH, Lasiecka I, Webster JT. Nonlinear Elastic Plate in a Flow of Gas: Recent Results and Conjectures. Applied Mathematics and Optimization. 2016 Jun 1;73(3):475–500.
Chueshov, I., et al. “Nonlinear Elastic Plate in a Flow of Gas: Recent Results and Conjectures.” Applied Mathematics and Optimization, vol. 73, no. 3, June 2016, pp. 475–500. Scopus, doi:10.1007/s00245-016-9349-1.
Chueshov I, Dowell EH, Lasiecka I, Webster JT. Nonlinear Elastic Plate in a Flow of Gas: Recent Results and Conjectures. Applied Mathematics and Optimization. 2016 Jun 1;73(3):475–500.
Journal cover image

Published In

Applied Mathematics and Optimization

DOI

EISSN

1432-0606

ISSN

0095-4616

Publication Date

June 1, 2016

Volume

73

Issue

3

Start / End Page

475 / 500

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics