UPPER SEMI-CONTINUITY AND REGULARITY OF RANDOM ATTRACTORS FOR STOCHASTIC FRACTIONAL POWER DISSIPATIVE EQUATIONS

Hong Lu; Mingji Zhang

doi:10.11948/20230177

2024 Volume 14 Issue 2

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Hong Lu, Mingji Zhang. UPPER SEMI-CONTINUITY AND REGULARITY OF RANDOM ATTRACTORS FOR STOCHASTIC FRACTIONAL POWER DISSIPATIVE EQUATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 816-846. doi: 10.11948/20230177

Citation:

Hong Lu, Mingji Zhang. UPPER SEMI-CONTINUITY AND REGULARITY OF RANDOM ATTRACTORS FOR STOCHASTIC FRACTIONAL POWER DISSIPATIVE EQUATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 816-846. doi: 10.11948/20230177

UPPER SEMI-CONTINUITY AND REGULARITY OF RANDOM ATTRACTORS FOR STOCHASTIC FRACTIONAL POWER DISSIPATIVE EQUATIONS

Hong Lu^1,,
Mingji Zhang^2, ,

1.
School of Mathematics and Statistics, Shandong University, 264209 Weihai, China
2.
Department of Mathematics, New Mexico Institution of Mining and Technology, Socorro, NM 87801, USA

Author Bio: Email: ljwenling@163.com(H. Lu)
Corresponding author: Email: mingji.zhang@nmt.edu(M. Zhang)

Abstract

Abstract

This paper is devoted to the study of the asymptotic dynamics of stochastic fractional power dissipative equations with additive noise. A priori estimates for solutions are derived under certain growth conditions for the nonlinearity. We then prove that the random dynamical system has a unique $ (L^2, L^p) $-random attractor with $ p>2 $, and furthermore, the family of random attractors is upper semi-continuous and regular at any point in $ [0, \infty) $ under the topology of $ p $-norms.
- Stochastic fractional power dissipative equation /
- (L², L^p)-random attractor /
- upper semi-continuity /
- regularity
MSC: 37L55, 35B40, 60H15

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