본문 바로가기
KERD
논문KCI 등재

ENERGY DECAY RATE FOR THE KELVIN-VOIGT TYPE WAVE EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND ACOUSTIC BOUNDARY

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

In this paper, we study exponential stabilization of the vibra-tions of the Kelvin-Voigt type wave equation with Balakrishnan-Taylordamping and acoustic boundary in a bounded domain in Rn. To stabi-lize the systems, we incorporate separately, the internal material dampingin the model as like Kang [3]. Energy decay rate are obtained by theexponential stability of solutions by using multiplier technique.

Abstract

In this paper, we study exponential stabilization of the vibra-tions of the Kelvin-Voigt type wave equation with Balakrishnan-Taylordamping and acoustic boundary in a bounded domain in Rn. To stabi-lize the systems, we incorporate separately, the internal material dampingin the model as like Kang [3]. Energy decay rate are obtained by theexponential stability of solutions by using multiplier technique.

참고문헌 (17)

  1. A.T. Cousin, "On a system of Klein-Gordon type equations with acoustic boundary conditions", J. Math. Anal. Appl., 293, pp.293~309 (2004)
  2. A. V. Balakishnan, "Distributed parameter nonlinear damping models for ight structures", Damping 89 (1989), Flight Dynamics Lab and Air Force Wright Aeronautical Labs, WPAFB
  3. A. Vicente, "Wave equations with acoustic", memory boundary conditions, 2009, pp.27(3), 29~39[DOI]
  4. A. Zarai, "Global existence and polynominal decay for a problem Balakrishnan-Taylor damping", Archivum Mathematicum(BRNO), 46, pp.157~176 (2010)
  5. C.L. Frota, "Some nonlinear wave equations with acoustic boundary conditions", J. Differ. Equ., 164, pp.92~109 (2000)
  6. C.L. Frota, "Uniform stabilization for a hyperbolic equation with acoustic boundary conditions in simple connected domains", Progr. Nonlinear Differential Equa-tions Appl., 66, pp.297~312 (2005)
  7. G.C. Gorain, "Exponential eneragy decay estimates for the solutions of n-dimensional Kirchhoff type wave equation", Applied Mathematics and Computation, 117, pp.235~242 (2006)
  8. G. Kirchhoff, "Vorlesungen ubear Mathematische Physik" (1977), Mechanik(Teubner)
  9. H. Harrison, "Plane and circular motion of a string", J. Acoust. Soc. Am., 20, pp.874~875 (1948)
  10. J.Y. Park, "Some nonlinear wave equations with nonlinear memory source term and acoustic boundary conditions", Numer. Funct. Anal. Optim., 27, pp.889~903 (2006)
  11. J. Y. Park, "Decay rate estimates for wave equations of memory type with acoustic boundary conditions", Nonlinear Analysis : Theory, methods and Applications, 74(3), pp.993~998 (2011)
  12. Jong Yeoul Park, "Well-posedness and uniform decay rates for the Klein–Gordon equation with damping term and acoustic boundary conditions", Journal of Mathematical Physics, 50(1), pp.013506~ (2009), AIP Publishing[DOI]
  13. J.T. Beal, "Acoustic boundary conditions", Bull. Amer. Math. Soc., 80, pp.1276~1278 (1974)
  14. M.A. Horn, "Exact controllability and uniform stabilization of the Kirchhoff plate equation with boundary feedback acting via bending moments", J. Math. Anal. Appl., 167, pp.557~581 (1992)
  15. R. W. Bass, "Spillover, nonlinearity and exible structures, The Fourth NASA Workship on Computational Control of Flexible Aerospace Systems", NASA Conference Publication 10065, pp.1~14 (1991)
  16. 강용한, "Energy decay rate for the Kirchhoff type wave equation with acoustic boundary", East Asian Mathematical Journal, 28(3), pp.339~345 (2012), 영남수학회[DOI]
  17. 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[DOI]

관련 논문AI추천

이 간행물의 다른 논문 (9건)