Stability of Parallel Fluid Loaded Plates: A Nonlocal Approach

作者：Ashton A C L^*

来源：Studies in Applied Mathematics, 2010, 125(3): 301-329.

DOI：10.1111/j.1467-9590.2010.00490.x

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.

• 出版日期2010-10