Random attractors for a class of stochastic partial differential equations driven by general additive noise

By Benjamin Gess, Wei David Liu, M. Roeckner. 2010

143 citations recorded by the source corpus.

Abstract The existence of random attractors for a large class of stochastic partial differential equations (SPDE) driven by general additive noise is established. The main results are applied to various types of SPDE, as e.g. stochastic reaction–diffusion equations, the stochastic p -Laplace equation and stochastic porous media equations. Besides classical Brownian motion, we also include space-time fractional Brownian motion and space-time Levy noise as admissible random perturbations. Moreover, cases where the attractor consists of a single point are also investigated and bounds for the speed of attraction are obtained.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/064e81ab2463d365ab65cfe447293c3e451ff7a9

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Citations in the corpus

Well-posedness of stochastic partial differential equations with Lyapunov condition (2013, background): “[1,12,28]).”
Existence and continuity of bi-spatial random attractors and application to stochastic semilinear Laplacian equations (2015, background): “The (single-spatial) random attractor for such equations (with slightly different principal parts) in a bounded domain has been considered in [18–20,33,39] recently.”
Data-driven non-Markovian closure models (2014, background): “Furthermore, the random-attractor arguments used here are not limited to the case of white noise and can be used to ensure the existence of non-degenerate solutions for MSMs driven by more general noises [85], as proposed in [83]; see also Remark 1.”
Well-posedness of stochastic partial differential equations with fully local monotone coefficients (2022, background): “see [48, 27, 5] for regularity of solutions, [18, 74, 47, 19, 88, 52, 61, 87, 37, 38] for large deviation principle, [31, 32, 33, 78, 65, 4, 90] for numerical approximation, [84, 46, 85, 86] for the Harnack inequality, gradient estimates, invariant measure and ergodicity, [28, 29] for random attract”
Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains (2013, background): “Since then, such attractors for autonomous stochastic PDEs have been studied in [6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 31] in bounded domains, and in [4, 33, 34] in unbounded domains.”
Strong solutions for SPDE with locally monotone coefficients driven by L\'{e}vy noise (2011, unknown): “[43, 27, 45, 48, 46, 18]).”
Asymptotic behavior of random fitzhugh-nagumo systems driven by colored noise (2017, background): “The concept of random attractors was introduced in [18, 21, 44] and further studied in [6, 7, 8, 9, 11, 12, 13, 15, 16, 18, 22, 23, 24, 26, 32, 37, 40, 50, 51] for the autonomous stochastic equations; and in [2, 14, 19, 27, 28, 52, 53, 54] for the non-autonomous stochastic equations.”