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

Tae Gab Ha

doi:10.3934/dcds.2016100

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

Tae Gab Ha^*

^*Corresponding author for this work

Department of Mathematics

Pusan National University

Research output: Contribution to journal › Journal article › peer-review

10 Scopus citations

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].

Original language	English
Pages (from-to)	6899-6919
Number of pages	21
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	36
Issue number	12
DOIs	https://doi.org/10.3934/dcds.2016100
State	Published - 2016.12

Keywords

Acoustic boundary conditions
General decay rates
Global existence
Variable coefficients
Viscoelastic equation

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10.3934/dcds.2016100

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title = "Global existence and general decay estimates for the viscoelastic equation with acoustic boundary conditions",

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].",

keywords = "Acoustic boundary conditions, General decay rates, Global existence, Variable coefficients, Viscoelastic equation",

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year = "2016",

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T1 - Global existence and general decay estimates for the viscoelastic equation with acoustic boundary conditions

AU - Ha, Tae Gab

PY - 2016/12

Y1 - 2016/12

N2 - 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].

AB - 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].

KW - Acoustic boundary conditions

KW - General decay rates

KW - Global existence

KW - Variable coefficients

KW - Viscoelastic equation

UR - https://www.scopus.com/pages/publications/84992036168

U2 - 10.3934/dcds.2016100

DO - 10.3934/dcds.2016100

M3 - Journal article

AN - SCOPUS:84992036168

SN - 1078-0947

VL - 36

SP - 6899

EP - 6919

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 12

ER -

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

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Keywords

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