Provider: Ingenta Connect
Database: Ingenta Connect
Content: application/x-research-info-systems
TY - ABST
AU - Ashton, A. C. L.
TI - Stability of Parallel Fluid Loaded Plates: A Nonlocal Approach
JO - Studies in Applied Mathematics
PY - 2010-10-01T00:00:00///
VL - 125
IS - 3
SP - 301
EP - 329
N2 - 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 *C*_{0} -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.
UR - https://www.ingentaconnect.com/content/bpl/sapm/2010/00000125/00000003/art00004
M3 - doi:10.1111/j.1467-9590.2010.00490.x
UR - https://doi.org/10.1111/j.1467-9590.2010.00490.x
ER -