Attractors for a damped stochastic wave equation of sine-Gordon type with sublinear multiplicative noise. (English) Zbl 1103.37053
Summary: The existence of compact random attractors is proved for a damped stochastic wave equation of sine-Gordon type with sublinear multiplicative noise under homogeneous Dirichlet boundary condition. To be important, in this note a precise estimate of upper bound of Hausdorff dimension of the random attractors is obtained in lower dimension.
MSC:
| 37L55 | Infinite-dimensional random dynamical systems; stochastic equations |
| 37L30 | Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35B41 | Attractors |
| 35L70 | Second-order nonlinear hyperbolic equations |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
References:
| [1] | Chepyzhov V., Indiana Univ. Math. Journal 140 pp 193– (1991) |
| [2] | Témam R., Infinite-Dimensional Dynamical Systems in Mechanics and Physics. (1997) |
| [3] | DOI: 10.1007/BF01193705 · Zbl 0819.58023 · doi:10.1007/BF01193705 |
| [4] | DOI: 10.1007/BF02219225 · Zbl 0884.58064 · doi:10.1007/BF02219225 |
| [5] | Flandoli F., Stochastics and Stoch. Reports 59 pp 21– (1996) · Zbl 0870.60057 · doi:10.1080/17442509608834083 |
| [6] | Schmalfß B., Stochastic Anal. Appl. 17 pp 1075– (1999) · Zbl 0944.60071 · doi:10.1080/07362999908809649 |
| [7] | DOI: 10.1016/S0021-7824(99)80001-4 · Zbl 0919.58044 · doi:10.1016/S0021-7824(99)80001-4 |
| [8] | Debussche A., Stoch. Anal. Appl. 15 pp 473– (1997) · Zbl 0888.60051 · doi:10.1080/07362999708809490 |
| [9] | DOI: 10.2140/pjm.2004.216.63 · Zbl 1065.37057 · doi:10.2140/pjm.2004.216.63 |
| [10] | Fan X., Applied Mathematics and Computation 158 pp 253– (2004) · Zbl 1107.35084 · doi:10.1016/j.amc.2003.08.147 |
| [11] | Ghidaglia J.M., J. Math. Pure Appl. 66 pp 273– (1987) |
| [12] | Zhou S., J. Math. Anal. Appl. 275 pp 850– (2002) · Zbl 1072.35560 · doi:10.1016/S0022-247X(02)00437-7 |
| [13] | Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Eqautions (1983) · Zbl 0516.47023 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
