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Random Attractor Family for the Kirchhoff Equation of Higher Order with White Noise
Department of Mathematics, Yunnan University, Kunming, China
Department of Mathematics, Yunnan University, Kunming, China
- 1 Department of Mathematics, Yunnan University, Kunming, China
- 2 Department of Mathematics, Yunnan University, Kunming, China
Advances in Pure Mathematics·Volume 09 (2019)·Pages 404–414·Published 11 April 2019·DOI10.4236/apm.2019.94018
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Abstract
The existence of random attractor family for a class of nonlinear high-order Kirchhoff equation stochastic dynamical systems with white noise is studied. The Ornstein-Uhlenbeck process and the weak solution of the equation are used to deal with the stochastic terms. The equation is transformed into a general stochastic equation. The bounded stochastic absorption set is obtained by estimating the solution of the equation and the existence of the random attractor family is obtained by isomorphic mapping method. Temper random compact sets of random attractor family are obtained.
KeywordsStochastic Dynamical SystemWhite NoiseRandom Attractor FamilyWiener ProcessOrnstein-Uhlenbeck Process
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