Asymptotic analysis of a thin fluid layer-elastic plate interaction problem. Issue 11 (18th August 2019)

• Record Type: Journal Article
• Authors: Ćurković, A.; Marušić-Paloka, E.
• Is Part Of: Applicable analysis. Volume 98:Issue 11(2019)
• Page Start: 2118
• Page End: 2143
• Publication Date: 2019-08-18
• Subjects: Fluid-structure interaction -- Stokes equations -- elastic plate -- asymptotic analysis; 74F10 -- 35Q30 -- 76M45; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1451640
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We study the nonstationary flow of an incompressible fluid in a thin rectangle with an elastic plate as the upper part of the boundary. The flow is governed by a time-dependent pressure drop and an external force and it is modeled by Stokes equations. The dynamic of this fluid–structure interaction problem is studied in the limit when the thickness of the fluid domain tends to zero. Using the asymptotic techniques, we obtain for the effective plate displacement a sixth-order parabolic equation with a non standard boundary conditions. Results on existence, uniqueness and regularity of the solution are proved. The approximation is justified through a weak convergence theorem.