@article {Ashton:2010:0022-2526:301,
title = "Stability of Parallel Fluid Loaded Plates: A Nonlocal Approach",
journal = "Studies in Applied Mathematics",
parent_itemid = "infobike://bpl/sapm",
publishercode ="bp",
year = "2010",
volume = "125",
number = "3",
publication date ="2010-10-01T00:00:00",
pages = "301-329",
itemtype = "ARTICLE",
issn = "0022-2526",
eissn = "1467-9590",
url = "https://www.ingentaconnect.com/content/bpl/sapm/2010/00000125/00000003/art00004",
doi = "doi:10.1111/j.1467-9590.2010.00490.x",
author = "Ashton, A. C. L.",
abstract = "We consider the motion of a collection of fluid loaded elastic plates, situated horizontally in an infinitely long channel. We use a new, unified approach to boundary value problems, introduced by A.S. Fokas in the late 1990s, and show the problem is equivalent to a system of one-parameter integral equations. We give a detailed study of the linear problem, providing explicit solutions and well-posedness results in terms of standard Sobolev spaces. We show that the associated Cauchy problem is completely determined by a matrix, which depends solely on the mean separation of the plates and the horizontal velocity of each of the driving fluids. This matrix corresponds to the infinitesimal generator of the C0 -semigroup for the evolution equations in Fourier space. By analyzing the properties of this matrix, we classify necessary and sufficient conditions for which the problem is asymptotically stable.",
}