Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (1): 122-133.
Previous Articles Next Articles
Feng Baowei1, Su Keqin2
Received:2016-10-28
Revised:2017-04-01
Online:2018-02-26
Published:2018-02-26
Supported by:CLC Number:
Feng Baowei, Su Keqin. Uniform Decay for a Fourth-Order Viscoelastic Equation with Density in Rn[J].Acta mathematica scientia,Series A, 2018, 38(1): 122-133.
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
| [1] Messaoudi S A. General decay of solutions of a viscoelastic equation. J Math Anal Appl, 2008, 341:1457-1467 [2] Messaoudi S A. General decay of the solution energy in a viscoelastic equation with a nonlinear source. Nonlinear Anal, 2008, 69:2589-2598 [3] Messaoudi S A. General decay of solutions of a weak viscoelastic equation. Arab J Sci Eng, 2011, 36:1569-1579 [4] Messaoudi S A, Tatar N E. Exponential and polynomial decay for a quasilinear viscoelastic equation. Nonlinear Anal, 2008, 68:785-793 [5] Messaoudi S A, Tatar N E. Global existence and uniform stability of solutions for a quasilinear viscoelastic problem. Math Methods Appl Sci, 2007, 30:665-680 [6] Messaoudi S A, Tatar N E. Global existence and asymptotic behavior for a nonlinear viscoelastic equation. Math Meth Sci Res J, 2003, 7:136-149 [7] Messaoudi S A, Al-Gharabli M M. A general decay result of a viscoelastic equation with past history and boundary feedback. Z Angew Math Phys, 2015, 66:1519-1528 [8] Guesmia A. Asymptotic stability of abstract dissipative systems with infinite memory. J Math Anal Appl, 2011, 382:748-760 [9] Woinowsky-Krieger S. The effect of axial force on the vibration of hinged hars. ASME J Appl Mech, 1950, 17:35-36 [10] Muñoz Rivera J E, Lapa E C, Barreto R. Decay rates for viscoelastic plates with memory. J Elasticity, 1996, 44:61-87 [11] Andrade D, Jorge Silva M A, Ma T F. Exponential stability for a plate equation with p-Laplacian and memory terms. Math Meth Appl Sci, 2012, 35:417-426 [12] Jorge Silva M A, Ma T F. On a viscoelastic plate equation with history setting and perturbation of p-Laplacian type. IMA J Appl Math, 2013, 78:1130-1146 [13] Ferreira J, Messaoudi S A. On the general decay of a nonlinear viscoelastic plate equation with a strong damping and p(x,t)-Laplacian. Nonlinear Anal, 2014, 104:40-49 [14] Jorge Silva M A, Munõz Rivera J E, Racke R. On a classes of nonlinear viscoelastic Kirchhoff plates:well-posedness and generay decay rates. Appl Math Optim, 2016, 73:165-194 [15] Guesmia A, Messaoudi S A. A new approach to the stability of an abstract system in the presence of infinite history. J Math Anal Appl, 2014, 416:212-228 [16] Cavalcanti M M, Domingos Cavalcanti V N, Soriano J A. Global existence and uniform decay rates to the Kirchhoff-Carrier equation with nonlinear dissipation. Adv Differential Equations, 2001, 6:85-116 [17] Cavalcanti M M, Domingos Cavalcanti V N, Ma T F. Exponential decay of the viscoelastic Euler-Bernoulli equation with a nonlocal dissipation in general domains. Differ Int Equ, 2004, 17:495-510 [18] Cavalcanti M M, Domingos Cavalcanti V N, Soriano J A. Global existence and asymptotic stability for the nonlinear and generalized damped extensible plate equation. Commun Contemp Math, 2004, 6:705-731 [19] Liu W, Li G, Hong L. Decay of solutions for a plate equation with p-Lalacian and memory term. Electron J Diff Equ, 2012, 129:1-5 [20] Ma T F. Boundary stabilization for a non-linear beam on elastic bearings. Math Meth Appl Sci, 2001, 24:583-594 [21] Ma T F, Narciso V. Global attractor for a model of extensible beam with nonlinear damping and source terms. Nonlinear Anal, 2010, 73:3402-3412 [22] Mustafa M I, Abusharkh G A. Plate equations with viscoelastic boundary damping. Indagationes Math, 2015, 26:307-323 [23] Karachalios N I, Stavrakakis N M. Existence of global attractor for semilinear dissipative wave equations on Rn. J Diff Equ, 1999, 157:183-205 [24] Papadopoulos P G, Stavrakakis N M. Global existence and blow-up results for an equation of Kirchhoff type on Rn. Topol Methods Nolinear Anal, 2001, 17:91-109 [25] Kafini M. Uniform decay of solutions to Cauchy viscoelastic problems with density. Elecron J Differ Equ, 2011, 2011:1-9 [26] Cavalcanti M M, Domingos Cavalcanti V N, Soriano J A. On existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions. J Math Anal Appl, 2003, 281:108-124 [27] Kafini M, Messaoudi S A. On the uniform decay in viscoelastic problem in Rn. Appl Math Comput, 2009, 215:1161-1169 [28] Kafini M, Messaoudi S A. A blow-up result in a Cauchy viscoelastic problem. Appl Math Lett, 2008, 21:549-553 [29] Kafini M, Messaoudi S A, Tatar N E. Decay rate of solutions for a Cauchy viscoelastic evolution equation. Indagationes Math, 2011, 22:103-115 [30] Zennir K. General decay of solutions for damped wave equation of Kirchhoff type with density in Rn. Ann Univ Ferrara, 2015, 61:381-394 [31] Zhou Y. A blow-up result for a nonlinear wave equation with damping and vanishing initial energy. Appl Math Lett, 2005, 18:281-286 [32] Zhou Y. Global existence and nonexistence for a nonlinear wave equation with damping and source terms. Math Nachr, 2005, 278:1341-1358 [33] Charão R C, Bisognin E, Bisognin V, Pazoto A F. Asymptotic behavior for a dissipative plate equation in Rn with periodic coefficients. Electron J Diff Equ, 2008, 2008:1-23 [34] Feng B. Global well-posedness and stability for a viscoelastic plate equation with a time delay. Math Prob Engin, 2015, Article ID:585021 [35] Babin A V, Vishik M I. Attractors for partial diffrential evolution equations in an unbounded domain. Proc Roy Soc Edinburgh Sect A, 1990, 116:221-243 |
| [1] | Liu Gongwei, Diao Lin. On Convexity for Energy Decay Rates of the Second-Order Evolution Equation with Memory and Time-Varying Delay [J]. Acta mathematica scientia,Series A, 2018, 38(3): 527-542. |
| [2] | Deng Jiqin, Deng Ziming. Existence and Uniqueness of Solutions for Nonlocal Cauchy Problem for Fractional Evolution Equations [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1157-1164. |
| [3] | ZHANG Shen-Yuan, QIU Jing-Hui. Monotone Minkowski Functionals and Scalarizations of Henig Proper Efficiency [J]. Acta mathematica scientia,Series A, 2014, 34(3): 581-592. |
| [4] | YE Yu-Lin, DOU Chang-Sheng, JIU Quan-Sen. LOCAL WELL-POSEDNESS TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY [J]. Acta mathematica scientia,Series A, 2014, 34(3): 851-871. |
| [5] | LING Neng-Xiang, DING Jie. Asymptotic Properties of Conditional Density Estimation for Dependence Functional Data [J]. Acta mathematica scientia,Series A, 2012, 32(3): 547-556. |
| [6] | XIE Feng-Fan, HU Shi-Geng. On Buffon Problem for Bounded Lattices in E3 [J]. Acta mathematica scientia,Series A, 2011, 31(2): 410-414. |
| [7] | CHEN Chuan-Zhong, HAN Xin-Fang, MA Li. Some New Results about Asymptotic Properties of Additive Functionals of Brownian Motion [J]. Acta mathematica scientia,Series A, 2010, 30(6): 1485-1494. |
| [8] | ZHANG Chun-Guo, QIU Zhe-Yong. Energy Decay Estimates for the Nonhomogeneous Timoshenko Beam with a Local Nonlinear Feedback [J]. Acta mathematica scientia,Series A, 2010, 30(1): 197-206. |
| [9] | CHAI Fu-Jie. The Density of the Common Value-points of Two Algebroidal Functions and the Uniqueness Theorems [J]. Acta mathematica scientia,Series A, 2009, 29(6): 1765-1770. |
| [10] | LI Li-Na, GAO Fu-Qing. Rates of Strong Uniform Consistency for Kernel Density Estimators of Directional Data [J]. Acta mathematica scientia,Series A, 2009, 29(3): 707-715. |
| [11] |
Zhang Ting.
Discontinuous Solutions of the Navier-Stokes Equations for Compressible Flow with Density-Dependent Viscosity [J]. Acta mathematica scientia,Series A, 2008, 28(2): 214-221. |
| [12] | Liu Xiaopeng; Liu Kunhui. The Changes of F Distribution Density Curve [J]. Acta mathematica scientia,Series A, 2007, 27(2): 331-342. |
| [13] | LIU Xiao-Feng, LIU Kun-Hui. The Effects of Changes of Parameters on Distribution Density Function [J]. Acta mathematica scientia,Series A, 2005, 25(7): 1012-1029. |
| [14] | WANG Hai-Bin, HUI Bo-Cheng, CHEN Gao-Qiu. The Approximate Third order Moments and Bispectral Density of LTBL Model [J]. Acta mathematica scientia,Series A, 2004, 24(4): 501-512. |
| [15] | Wang Xiaoming. Strong Consistency for Kernel Neighbor Estimator of Density Function of spherical Data [J]. Acta mathematica scientia,Series A, 2000, 20(3): 386-393. |
|