Random attractors for stochastic reaction–diffusion equations on unbounded domains

By Peter W. Bates, Kening Lu, Bixiang Wang. 2009

404 citations recorded by the source corpus.

The existence of a pullback attractor is established for a stochastic reaction–diffusion equation on all n-dimensional space. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears as spatially distributed temporal white noise. The reaction–diffusion equation is recast as a random dynamical system and asymptotic compactness for this is demonstrated by using uniform a priori estimates for far-field values of solutions.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/dbd650b61b9ca99511b133942a80c31ea5d7114d

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In Computational Theory and Mathematics

1. Bixiang Wang
2. Shengfan Zhou
3. Anhui Gu
4. Kening Lu
5. Yangrong Li
6. Andrew L. Krause
7. Min Zhao
8. Peter W. Bates

In Computer Networks and Communications

1. Bixiang Wang
2. Shengfan Zhou
3. Anhui Gu
4. Kening Lu
5. Peter W. Bates
6. Yangrong Li
7. Andrew L. Krause
8. Min Zhao

In Control and Systems Engineering

1. Bixiang Wang
2. Shengfan Zhou
3. Anhui Gu
4. Kening Lu
5. Yangrong Li
6. Andrew L. Krause
7. Peter W. Bates
8. Min Zhao

Citations in the corpus

• Existence and continuity of bi-spatial random attractors and application to stochastic semilinear Laplacian equations (2015, background): “see [4]).”
• Attractors of non-autonomous stochastic lattice systems in weighted spaces (2014, background): “The existence of such attractors was proved in [11, 12, 13, 14, 15, 26, 27, 28, 33, 34, 41, 46, 47, 51] for autonomous stochastic PDEs defined in bounded domains, and in [8, 55, 56] for PDEs defined on unbounded domains.”
• 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.”
• 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.”