본문 바로가기
KERD
논문KCI 등재

STABILITY FOR A VISCOELASTIC PLATE EQUATION WITH p-LAPLACIAN

박선혜
대한수학회 (The Korean Mathematical Society)|2015.05|대한수학회보 (Bulletin of the KMS)|제52권 제3호|pp. 907-914

2

조회

0

다운로드

1

인용

0

참고문헌

키워드

plate equationp-laplacianweak viscoelasticitygeneral decay
주제분류수학

초록

In this paper, we consider a viscoelastic plate equation with p-Laplacian u′′ + △2u − div(|∇u|p−2∇u) + σ(t) ∫ t 0 g(t − s)△u(s)ds − △u′ = 0. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of both σ and g.

Abstract

In this paper, we consider a viscoelastic plate equation with p-Laplacian u′′ + △2u − div(|∇u|p−2∇u) + σ(t) ∫ t 0 g(t − s)△u(s)ds − △u′ = 0. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of both σ and g.

참고문헌 (12)

  1. D. Andrade, "Exponential stability for a plate equation with p-Laplacian and memory terms", Math. Methods Appl. Sci, 35(4), pp.417~426 (2012)
  2. M. M. Cavalcanti, "Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping", Differential Integral Equations, 14(1), pp.85~116 (2001)
  3. M. M. Cavalcanti, "General decay rate estimates for viscoelastic dissipative systems", Nonlinear Anal, 68(1), pp.177~193 (2008)
  4. A. Guesmia, "General energy decay estimates of Timoshenko sys-tems with frictional versus viscoelastic damping", Math. Methods Appl. Sci, 32(16), pp.2102~2122 (2009)
  5. T. F. Ma, "On weak solutions for an evolution equation with exponential nonlinearities", Nonlinear Anal, 37(8), pp.1029~1038 (1999)
  6. S. A. Messaoudi, "General decay of solutions of a viscoelastic equation", J. Math. Anal. Appl, 341(2), pp.1457~1467 (2008)
  7. S. A. Messaoudi, "General decay of solutions of a weak viscoelastic equation", Arab. J. Sci. Eng, 36(8), pp.1569~1579 (2011)
  8. S. A. Messaoudi, "Exponential and polynomial decay for a quasilinear viscoelastic equation", Nonlinear Anal, 68(4), pp.785~793 (2008)
  9. J. Y. Park, "On weak solutions for hyperbolic differential inclusion with discontinuous nonlinearities", Nonlinear Anal, 55(1-2), pp.103~113 (2003)
  10. J. Y. Park, "General decay for quasilinear viscoelastic equations with nonlinear weak damping", J. Math. Phys, 50(8), pp.10~ (2009)
  11. Z. Yang, "Longtime behavior for a nonlinear wave equation arising in elasto-plastic flow", Math. Methods Appl. Sci, 32(9), pp.1082~1104 (2009)
  12. Z. Yang, "Global attractor for a class of Kirchhoff models", J. Math. Phys, 50(3), pp.29~ (2009)

관련 논문AI추천

GENERAL DECAY OF SOLUTIONS OF NONLINEAR VISCOELASTIC WAVE EQUATION강수진, 신기연영남수학회 · East Asian Mathematical Journal2016 · 제32권 제5호STABILIZATION FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH A NONLINEAR SOURCE김대욱영남수학회 · East Asian Mathematical Journal2016 · 제32권 제1호Global existence and asymptotic behavior of a plate equation with a constant delay term and logarithmic nonlinearitiesMelouka Remil대한수학회 · 대한수학회논문집2020 · 제35권 제1호ASYMPTIOTIC BEHAVIOR FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM김대욱영남수학회 · East Asian Mathematical Journal2016 · 제32권 제3호General Decay of Solutions for Viscoelastic Equation with Nonlinear Source Terms강수진, 신기연영남수학회 · East Asian Mathematical Journal2018 · 제34권 제5호Exponential Decay for the Solution of the Viscoelastic Kirchhoff Type Equation with Memory Condition at the Boundary김대욱영남수학회 · East Asian Mathematical Journal2018 · 제34권 제1호

이 간행물의 다른 논문 (28건)

THE FUNDAMENTAL THEOREM OF ALGEBRA AND THE DIVERGENCE OF RECIPROCALS OF PRIMES LOOKED AT THROUGH BERGMAN SPACESYunus E. Zeytuncupp. 699-705GENERALIZATION OF INEQUALITIES ANALOGOUS TO HERMITE–HADAMARD INEQUALITY VIA FRACTIONAL INTEGRALSKiran Nazeer, Muhammad Iqbal, Muhammad Iqbal Bhattipp. 707-716CLASSIFICATION ON ARITHMETIC FUNCTIONS AND CORRESPONDING FREE-MOMENT L-FUNCTIONS조일우pp. 717-734AN ESTIMATE OF HEMPEL DISTANCE FOR BRIDGE SPHERESAyako Idopp. 735-740THE n-TH TWISTED CHANGHEE POLYNOMIALS AND NUMBERS권종겸, 표성수, 박진우, 임석훈pp. 741-749
원문 보기