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Energy Decay Rates for the Kirchhoff Type Wave Equation with Balakrishnan-Taylor Damping and Acoustic Boundary

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영남수학회 (Youngnam Mathematical Society)|2014.05|East Asian Mathematical Journal|제30권 제3호|pp. 249-258|DOI http://dx.doi.org/10.7858/eamj.2014.015

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키워드

StabilizationEnergy decayKirchhoff typeLyapunov functionalBalakrishnan-Taylor dampingAcoustic boundary
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초록

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with Balakrishnan-Taylor damping and acoustic boundary in a bounded domain in $R^n $. To stabilize the systems, we incorporate separately, the passive viscous damping in the model as like Kang\cite{A13}. Energy decay rates are obtained by the uniform exponential stability of solutions by using multiplier technique.

Abstract

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with Balakrishnan-Taylor damping and acoustic boundary in a bounded domain in $R^n $. To stabilize the systems, we incorporate separately, the passive viscous damping in the model as like Kang\cite{A13}. Energy decay rates are obtained by the uniform exponential stability of solutions by using multiplier technique.

참고문헌 (17)

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  13. 강용한, "Energy decay rate for the Kirchhoff type wave equation with acoustic boundary", East Asian Mathematical Journal, 28(3), pp.339~345 (2012), 영남수학회
  14. 서영일, "ENERGY DECAY RATES FOR THE KELVIN-VOIGT TYPE WAVE EQUATION WITH ACOUSTIC BOUNDARY", Journal of the Korean Society for Industrial and Applied Mathematics, 16(2), pp.85~91 (2012), 한국산업응용수학회
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관련 논문AI추천

ENERGY DECAY RATE FOR THE KELVIN-VOIGT TYPE WAVE EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND ACOUSTIC BOUNDARY강용한영남수학회 · East Asian Mathematical Journal2016 · 제32권 제3호Energy decay rate for the Kirchhoff type wave equation with acoustic boundary강용한영남수학회 · East Asian Mathematical Journal2012 · 제28권 제3호Energy decay for a viscoelastic equation with Balakrishnan-Taylor damping involving infinite memory and nonlinear time-varying delay terms in dynamical boundaryAbita Rahmoune, Soufiane Benkouider대한수학회 · 대한수학회논문집2023 · 제38권 제3호STABILIZATION FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH A NONLINEAR SOURCE김대욱영남수학회 · East Asian Mathematical Journal2016 · 제32권 제1호ASYMPTIOTIC BEHAVIOR FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM김대욱영남수학회 · East Asian Mathematical Journal2016 · 제32권 제3호Exponential Decay for the Solution of the Viscoelastic Kirchhoff Type Equation with Memory Condition at the Boundary김대욱영남수학회 · East Asian Mathematical Journal2018 · 제34권 제1호

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