The analyticity and exponential decay of a Stokes-wave coupling system with viscoelastic damping in the variational framework

Jing Zhang

doi:10.3934/eect.2017008

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2017, Volume 6, Issue 1: 135-154. Doi: 10.3934/eect.2017008

This issue Previous Article On an inverse problem for fractional evolution equation Next Article

The analyticity and exponential decay of a Stokes-wave coupling system with viscoelastic damping in the variational framework

Jing Zhang

Department of Mathematics and Economics, Virginia State University, Petersburg, VA 23806, USA

Received: September 30, 2016

Revised: July 31, 2016

Published: March 2018

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Abstract

In this paper, we study a fluid-structure interaction model of Stokes-wave equation coupling system with Kelvin-Voigt type of damping. We show that this damped coupling system generates an analyticity semigroup and thus the semigroup solution, which also satisfies variational framework of weak solution, decays to zero at exponential rate.

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Mathematics Subject Classification: Primary: 35M10, 35B35; Secondary: 35A01.

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Figure 1. THE FLUID–STRUCTURE INTERACTION

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