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

Zhi Wang | Zendy; DU Xian-yun | Zendy

Open Access

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

Author(s) -

Zhi Wang,

DU Xian-yun

Publication year - 2017

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2017014

Subject(s) - pullback attractor , pullback , mathematics , uniqueness , forcing (mathematics) , attractor , mathematical analysis , compact space

In this paper, the existence and uniqueness of pullback attractors for the modified Swift-Hohenberg equation defined on R driven by both deterministic non-autonomous forcing and additive white noise are established. We first define a continuous cocycle for the equation in L(R), 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.

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