|
|
Pure Mathematics 2023
具有奇异振荡外力的记忆型粘弹性发展方程一致吸引子的上半连续性
|
Abstract:
本文主要研究了具有奇异振荡外力项和弱阻尼项的记忆型粘弹性发展方程。首先证明了在外力项和记忆核满足恰当条件时方程一致吸引子 Aε在空间H = H01(Ω)×H01(Ω)×M中的一致有界性, 进而证明了当ε→0+ 时一致吸引子的上半连续性。
This paper is concerned with the development of memory viscoelastic equation with singularly oscillating external force terms and weak damping terms. First, we prove the consistent boundedness of the uniform attractor A\" of the equation in H = H01(Ω)×H01(Ω)×M when the external force term and the memory kernel satisfy the appropriate conditions, and then the upper semicontinuity of the uniform attractor when ε→0+ is achieved.
| [1] | Chepyzhov, V.V. and Vishik, M.I. (1994) Attractors of Nonautonomous Dynamical Systems
and Their Dimension. Journal de Mathematiques Pures et Appliquees, 73, 279-333. |
| [2] | Sun, C.Y., Cao, D.M. and Duan, J.Q. (2007) Uniform Attractors for Nonautonomous Wave
Equations with Nonlinear Damping. SIAM Journal on Applied Dynamical Systems, 6, 293-318.
https://doi.org/10.1137/060663805 |
| [3] | Chepyzhov, V.V. and Vishik, M.J. (2001) Attractors for Equations of Mathematical Physics.
In: American Mathematical Society Colloquium Publications, AMS.
https://doi.org/10.1090/coll/049 |
| [4] | Song, X.L. and Hou, Y.R. (2015) Uniform Attractors for Three-Dimensional Navier-Stokes
Equations with Nonlinear Damping. Journal of Mathematical Analysis and Applications, 422,
337-351. https://doi.org/10.1016/j.jmaa.2014.08.044 |
| [5] | Qin, Y.M., Feng, B.W. and Zhang, M. (2014) Uniform Attractors for a Nonautonomous Vis-
coelastic Equation with a Past History. Nonlinear Analysis, 101, 1-15.
https://doi.org/10.1016/j.na.2014.01.006 |
| [6] | Munoz Rivera, J.E. (1994) Asymptotic Behaviour in Linear Viscoelasticity. Quarterly of Applied Mathematics, 52, 629-648. https://doi.org/10.1090/qam/1306041 |
| [7] | Park, J.Y. and Kang, J.R. (2010) Global Attractor for Hyperbolic Equation with Nonlinear
Damping and Linear Memory. Science China Mathematics, 53, 1531-1539.
https://doi.org/10.1007/s11425-010-3110-z |
| [8] | Guesmia, A. and Messaoudi, S.A. (2012) A General Decay Result for a Viscoelastic Equa-
tion in the Presence of Past and Finite History Memories. Nonlinear Analysis: Real World
Applications, 13, 476-485. https://doi.org/10.1016/j.nonrwa.2011.08.004 |
| [9] | Munoz Rivera, J.E., Lapa, E.C. and Barreto, R. (1996) Decay Rates for Viscoelastic Plates
with Memory. Journal of Elasticity, 44, 61-87. https://doi.org/10.1007/BF00042192 |
| [10] | Conti, M., Ma, T.F., Marchini, E.M. and Seminario Huertas, P.N. (2018) Asymptotics of
Viscoelastic Materials with Nonlinear Density and Memory Effects. Journal of Differential
Equations, 264, 4235-4259. https://doi.org/10.1016/j.jde.2017.12.010 |
| [11] | Zhang, J.W., Liu, Z.M. and Huang, J.H. (2023) Upper Semicontinuity of Optimal Attractors for Viscoelastic Equations Lacking Strong Damping. Applicable Analysis, 102, 3609-3628.
https://doi.org/10.1080/00036811.2022.2088532 |
| [12] | Qin, Y.M., Zhang, J.P. and Sun, L.L. (2013) Upper Semicontinuity of Pullback Attractors
for a Non-Autonomous Viscoelastic Equation. Applied Mathematics and Computation, 223,
362-376. https://doi.org/10.1016/j.amc.2013.08.034 |
| [13] | Chepyzhov, V.V., Conti, M. and Pata, V. (2017) Averaging of Equations of Viscoelasticity
with Singularly Oscillating External Forces. Journal de Mathematiques Pures et Appliquees,
108, 841-868. https://doi.org/10.1016/j.matpur.2017.05.007 |
| [14] | Temam, R. (1997) Infinite-Dimensional Dynamical Systems in Mechanics and Physics. 2nd
Edition, Springer, New York. |
