Random Attractor for Stochastic Partial Functional Differential Equations With Infinite Delay

You, Honglian; Yuan, Rong

doi:10.4134/bkms.2014.51.5.1469

Cited by 2 publications

(1 citation statement)

References 19 publications

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“…Random attractor was first studied in [20,22,69]. It is a very important concept of capturing the long-time behavior of random dynamical systems (RDS) and there are many results on existence and properties of random attractors for various SPDE [15,31,32,36,38,40,41,48,57,59,70,77,84,86,87,90].…”

Section: Introductionmentioning

confidence: 99%

Random attractors for locally monotone stochastic partial differential equations

Gess¹,

Liu²,

Schenke³

2019

Preprint

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We prove the existence of random dynamical systems and random attractors for a large class of locally monotone stochastic partial differential equations perturbed by additive Lévy noise. The main result is applicable to various types of SPDE such as stochastic Burgers type equations, stochastic 2D Navier-Stokes equations, the stochastic 3D Leray-α model, stochastic power law fluids, the stochastic Ladyzhenskaya model, stochastic Cahn-Hilliard type equations, stochastic Kuramoto-Sivashinsky type equations, stochastic porous media equations and stochastic p-Laplace equations.

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Section: Introductionmentioning

confidence: 99%

Random attractors for locally monotone stochastic partial differential equations

Gess¹,

Liu²,

Schenke³

2019

Preprint

View full text Add to dashboard Cite

show abstract

Random attractors for locally monotone stochastic partial differential equations

Gess

Liu

Schenke

2020

Journal of Differential Equations

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The existence of random attractors for singular stochastic partial differential equations (SPDE) perturbed by general additive noise is proven. The drift is assumed only to satisfy the standard assumptions of the variational approach to SPDE with compact embeddings in the Gelfand triple and singular coercivity. For ergodic, monotone, contractive random dynamical systems it is proven that the attractor consists of a single random point. In case of real, linear multiplicative noise finite time extinction is obtained. Applications include stochastic generalized fast diffusion equations and stochastic generalized singular p-Laplace equations perturbed by Lévy noise with jump measure having finite first and second moments.2000 Mathematics Subject Classification AMS: Primary: 37L55, 60H15. Secondary: 37L30.

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Random Attractor for Stochastic Partial Functional Differential Equations With Infinite Delay

Cited by 2 publications

References 19 publications

Random attractors for locally monotone stochastic partial differential equations

Random attractors for locally monotone stochastic partial differential equations

Random attractors for locally monotone stochastic partial differential equations

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