Global existence and general decay estimates for the viscoelastic equation with acoustic boundary conditions

Tae Gab Ha

doi:10.3934/dcds.2016100

Article Contents

2016, Volume 36, Issue 12: 6899-6919. Doi: 10.3934/dcds.2016100

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Global existence and general decay estimates for the viscoelastic equation with acoustic boundary conditions

Tae Gab Ha^1,

1.
Department of Mathematics, Pusan National University, Busan, 609-735

Received: January 31, 2016

Revised: June 30, 2016

Published: May 2017

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Abstract

In this paper, we consider the viscoelastic equation with damping and source terms and acoustic boundary conditions. We prove a global existence of solutions and uniform decay rates of the energy without imposing any restrictive growth assumption on the damping term and weakening of the usual assumptions on the relaxation function. This paper is to improve the result of [4] by applying the method developed in [17].

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Mathematics Subject Classification: Primary: 35L70; Secondary: 35B40.

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