PULLBACK ATTRACTORS FOR MODIFIED SWIFT-HOHENBERG EQUATION ON UNBOUNDED DOMAINS WITH NON-AUTONOMOUS DETERMINISTIC AND STOCHASTIC FORCING TERMS

Zhi Wang; Xianyun Du

doi:10.11948/2017014

2017 Volume 7 Issue 1

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Zhi Wang, Xianyun Du. PULLBACK ATTRACTORS FOR MODIFIED SWIFT-HOHENBERG EQUATION ON UNBOUNDED DOMAINS WITH NON-AUTONOMOUS DETERMINISTIC AND STOCHASTIC FORCING TERMS[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 207-223. doi: 10.11948/2017014

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Zhi Wang, Xianyun Du. PULLBACK ATTRACTORS FOR MODIFIED SWIFT-HOHENBERG EQUATION ON UNBOUNDED DOMAINS WITH NON-AUTONOMOUS DETERMINISTIC AND STOCHASTIC FORCING TERMS[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 207-223. doi: 10.11948/2017014

PULLBACK ATTRACTORS FOR MODIFIED SWIFT-HOHENBERG EQUATION ON UNBOUNDED DOMAINS WITH NON-AUTONOMOUS DETERMINISTIC AND STOCHASTIC FORCING TERMS

College of Applied Mathematics, Chengdu university of information technology, Chengdu, Sichuan 610225, China

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Abstract

Abstract

In this paper, the existence and uniqueness of pullback attractors for the modified Swift-Hohenberg equation defined on Rn driven by both deterministic non-autonomous forcing and additive white noise are established. We first define a continuous cocycle for the equation in L²(Rⁿ), and we prove the existence of pullback absorbing sets and the pullback asymptotic compactness of solutions when the equation with exponential growth of the external force. The long time behaviors are discussed to explain the corresponding physical phenomenon.
- Swift-Hohenberg equation /
- random dynamical systems /
- continuous cocycle /
- pullback attractors /
- asymptotic compactness
MSC: 35R60;37L55;60H10

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References

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