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Random Attractor Family for a Class of Stochastic Higher-Order Kirchhoff Equations

Author

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  • Guoguang Lin
  • Liping Guan

Abstract

A class of stochastic dynamical systems with strong damped stochastic higher order Kirchhoff equation solutions with white noise is studied. Firstly, the equation is transformed into a stochastic equation with random variables as parameters and without noise by using Ornstein-Uhlenbeck process. Secondly, the bounded stochastic absorption set is obtained by estimating the solution of the equation. Finally, the stochastic dynamical system is obtained by using the isomorphic mapping method and the compact embedding theorem. It is progressively compact, thus proving the existence of random attractors.

Suggested Citation

  • Guoguang Lin & Liping Guan, 2019. "Random Attractor Family for a Class of Stochastic Higher-Order Kirchhoff Equations," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(3), pages 23-33, June.
    • Handle: RePEc:ibn:jmrjnl:v:11:y:2019:i:3:p:23
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    More about this item

    Keywords

    stochastic Kirchhoff equation; random attractor family; Wiener process; Ornstein-Uhlenbeck process;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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