Appl Math Optim (2016) 73:475–500
Nonlinear Elastic Plate in a Flow of Gas: Recent Results
· Earl H. Dowell
· Justin T. Webster
Published online: 30 March 2016
© Springer Science+Business Media New York 2016
Abstract 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 discus-
sion here is on the interesting mathematical aspects of physical phenomena occurring
in aeroelasticity, such as ﬂutter and divergence. This leads to a partial differential equa-
tion 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.
In memory of A.V. Balakrishnan.
Justin T. Webster
Earl H. Dowell
Kharkov National University, Kharkov, Ukraine
Duke University, Durham, NC, USA
University of Memphis, Memphis, TN, USA
IBS, Polish Academy of Sciences, Warsaw, Poland
College of Charleston, Charleston, SC, USA