一类广义非线性Kirchhoff型方程的整体吸引子
Global Attractor for a Class of Nonlinear Generalized Kirchhoff Equation
摘要:
该文研究了广义Kirchhoff型方程：u
tt+αu
t−βΔu
t−Φ
(‖∇u‖
2)Δu+
(1+|u|
2)p-1u=f
(x
)的初边值问题的解的长时间行为。证明上述问题对应的算子半群存在((H
2⌒H
10)ΧH
10，(H
2⌒H
10)xH
2⌒H
10))-整体吸引子。
Abstract:
The paper studies the longtime behavior of solutions to the initial boundary value problem (IBVP) for a class of Kirchhoff models: utt+αut−βΔut−Φ(‖∇u‖2)Δu+(1+|u|2)p-1u=f(x). We show the semigroup has a ((H2⌒H10)ΧH10，(H2⌒H10)xH2⌒H10))-global attractor.
参考文献
|
[1]
|
Yang, Z.J., Feng, N. and Ma, T.F. (2015) Global Attractor for the Generalized Double Dispersion Equation. Nonlinear Analysis, 115, 103-116.
[Google Scholar] [CrossRef]
|
|
[2]
|
杨志坚, 程建玲. Kirchhoff型方程解的渐近行为[J]. 数学物理学报, 2011, 31A(4): 1008-1021.
|
|
[3]
|
Pata, V. and Zelik, S. (2006) Smooth Attractors for Strongly Damped Wave Equations. Nonlinearity, 19, 1495-1506.
[Google Scholar] [CrossRef]
|
|
[4]
|
Lin, G.G. (2011) Nonlinear Evolution Equation. Yunnan University Press, Kunming.
|
|
[5]
|
Chueshov, I. (2012) Long-Time Dynamics of Kirchhoff Wave Models with Strong Nonlinear Damping. Journal of Differential Equations, 252, 1229-1262.
[Google Scholar] [CrossRef]
|
|
[6]
|
Cheng, J.L. and Yang, Z.J. (2011) As-ymptotic Behavior of the Kirchhoff Type Equation. Acta Mathematica Scientia, 31A, 1008-1021.
|
|
[7]
|
Yang, Z.J. (2007) Longtime Behavior of the Kirchhoff Type Equation with Strong Damping on RN. Journal of Differential Equations, 242, 269-286.
[Google Scholar] [CrossRef]
|
|
[8]
|
Yang, M.H. and Sun, C.Y. (2009) Attractors for Strongly Damped Wave Equa-tions. Nonlinear Analysis, 10, 1097-1100.
[Google Scholar] [CrossRef]
|
|
[9]
|
Pata, V. and Squassina. M. (2005) On the Strongly Damped Wave Equation. Communications in Mathematical Physics, 253, 511-533.
[Google Scholar] [CrossRef]
|
|
[10]
|
Lv, P.H., Lu, J.X. and Lin, G.G. (2016) Global Attractor for a Class of Non-linear Generalized Kirchhoff Models. Journal of Advances in Mathematics, 12, 6452-6462.
|