Existence, Stability and Bifurcation of Random Complete and Periodic Solutions of Stochastic Parabolic Equations

By Bixiang Wang. 2013

55 citations recorded by the source corpus.

Abstract In this paper, we study the existence, stability and bifurcation of random complete and periodic solutions for stochastic parabolic equations with multiplicative noise. We first prove the existence and uniqueness of tempered random attractors for the stochastic equations and characterize the structures of the attractors by random complete solutions. We then examine the existence and stability of random complete quasi-solutions and establish the relations of these solutions and the structures of tempered attractors. When the stochastic equations are incorporated with periodic forcing, we obtain the existence and stability of random periodic solutions. For the stochastic Chafee–Infante equation, we further establish the multiplicity and stochastic bifurcation of complete and periodic solutions.

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

View Paper: https://www.semanticscholar.org/paper/3ccd7ba64f66c99f849c270b5fcfc9f544f9a16b

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In Applied Mathematics

1. Chunrong Feng
2. Huaizhong Zhao
3. Yue Wu
4. Kening Lu
5. Bixiang Wang
6. Xiaohu Wang

In Computational Theory and Mathematics

1. Bixiang Wang
2. Chunrong Feng
3. Huaizhong Zhao
4. Xiaohu Wang
5. Kening Lu
6. Yue Wu
7. Shengfan Zhou
8. Anhui Gu

In Control and Systems Engineering

1. Bixiang Wang
2. Chunrong Feng
3. Huaizhong Zhao
4. Kening Lu
5. Xiaohu Wang
6. Yue Wu
7. Shengfan Zhou
8. Anhui Gu

Citations in the corpus

• Anticipating Random Periodic Solutions--I. SDEs with Multiplicative Linear Noise (2015, result): “There have been some more recent results including [8] on random attractors of the stochastic TJ model in climate dynamics, [27] on bifurcations of stochastic reaction diffusion equations and [5] on stochastic lattice systems.”
• Random periodic processes, periodic measures and ergodicity (2014, unknown): “progresses towards understanding random periodicity of various stochastic systems including Chekrouna, Simonnetc and Ghil [4] on random attractors of the stochastic TJ model in climate dynamics, Wang [30] on bifurcations of stochastic reaction diffusion equations, Feng, Wu and Zhao [13], [14], in the”
• Exponential Stability of Non-Autonomous Stochastic Delay Lattice Systems with Multiplicative Noise (2015, background): “For nonautonomous stochastic equations, the role of stationary solutions is replaced by random complete solutions (or random compete quasi-solutions) as in [34,36].”