Global existence and asymptotic behavior for a mildly degenerate kirchhoff wave equation with boundary damping

Qiong Zhang

doi:10.1090/S0033-569X-2012-01281-0

Global existence and asymptotic behavior for a mildly degenerate kirchhoff wave equation with boundary damping

Qiong Zhang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

In this article a degenerate nonlinear dissipative wave equation of Kirchhoff type with nonlinear boundary damping is considered. We prove the existence, uniqueness and regularity of the global solution of the system when the initial data are small enough and the geometry of the domain satisfies suitable assumptions. We also obtain the polynomial decay property of the global solution.

Original language	English
Pages (from-to)	253-267
Number of pages	15
Journal	Quarterly of Applied Mathematics
Volume	70
Issue number	2
DOIs	https://doi.org/10.1090/S0033-569X-2012-01281-0
Publication status	Published - 2012

Keywords

Boundary dissipation
Degenerate equation
Global existence
Kirchhoff equation
Polynomial decay

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10.1090/S0033-569X-2012-01281-0

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title = "Global existence and asymptotic behavior for a mildly degenerate kirchhoff wave equation with boundary damping",

abstract = "In this article a degenerate nonlinear dissipative wave equation of Kirchhoff type with nonlinear boundary damping is considered. We prove the existence, uniqueness and regularity of the global solution of the system when the initial data are small enough and the geometry of the domain satisfies suitable assumptions. We also obtain the polynomial decay property of the global solution.",

keywords = "Boundary dissipation, Degenerate equation, Global existence, Kirchhoff equation, Polynomial decay",

author = "Qiong Zhang",

year = "2012",

doi = "10.1090/S0033-569X-2012-01281-0",

language = "English",

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T1 - Global existence and asymptotic behavior for a mildly degenerate kirchhoff wave equation with boundary damping

AU - Zhang, Qiong

PY - 2012

Y1 - 2012

N2 - In this article a degenerate nonlinear dissipative wave equation of Kirchhoff type with nonlinear boundary damping is considered. We prove the existence, uniqueness and regularity of the global solution of the system when the initial data are small enough and the geometry of the domain satisfies suitable assumptions. We also obtain the polynomial decay property of the global solution.

AB - In this article a degenerate nonlinear dissipative wave equation of Kirchhoff type with nonlinear boundary damping is considered. We prove the existence, uniqueness and regularity of the global solution of the system when the initial data are small enough and the geometry of the domain satisfies suitable assumptions. We also obtain the polynomial decay property of the global solution.

KW - Boundary dissipation

KW - Degenerate equation

KW - Global existence

KW - Kirchhoff equation

KW - Polynomial decay

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U2 - 10.1090/S0033-569X-2012-01281-0

DO - 10.1090/S0033-569X-2012-01281-0

M3 - Article

AN - SCOPUS:84864943831

SN - 0033-569X

VL - 70

SP - 253

EP - 267

JO - Quarterly of Applied Mathematics

JF - Quarterly of Applied Mathematics

IS - 2

ER -

Global existence and asymptotic behavior for a mildly degenerate kirchhoff wave equation with boundary damping

Abstract

Keywords

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