Stability analysis of non-linear plates coupled with Darcy flows

Eugenio Aulisa; Akif Ibragimov; Emine Yasemen Kaya-Cekin

doi:10.3934/eect.2013.2.193

Article Contents

2013, Volume 2, Issue 2: 193-232. Doi: 10.3934/eect.2013.2.193

This issue Previous Article Preface: Introduction to the Special Volume on Nonlinear PDEs and Control Theory with Applications Next Article Rational decay rates for a PDE heat--structure interaction: A frequency domain approach

Stability analysis of non-linear plates coupled with Darcy flows

1.
Department of Mathematics and Statistics, Texas Tech University, Lubbock TX, 79409-1042
2.
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042

Received: October 2012

Revised: January 2013

Published: June 2013

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Abstract

In this paper we study the dynamical response of a non-linear plate with viscous damping perturbed in both vertical and axial directions and interacting with Darcy flow. We first consider the problem for non-linear elastic body with damping coefficient; existence and uniqueness of the solution for the steady state problem is proven. The stability of the dynamical non-linear plate problem under certain conditions on the applied loads is investigated. Second, we explore the fluid structure interaction problem with Darcy flow in porous media. Energy functional for the displacement field of the plate and the gradient pressure of the fluid flow is built in an appropriate Sobolev type norm. We show that for a class of boundary conditions the energy functional is limited by the flux of mass through the inlet boundary.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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