Zhao, Junyilang; Shen, Jun; Lu, Kening Persistence of \(C^1\) inertial manifolds under small random perturbations. (English) Zbl 07818497 J. Dyn. Differ. Equations 36, No. 1, Suppl., S333-S385 (2024). MSC: 60H15 60H40 35K58 37H10 37L55 35B42 PDFBibTeX XMLCite \textit{J. Zhao} et al., J. Dyn. Differ. Equations 36, No. 1, S333--S385 (2024; Zbl 07818497) Full Text: DOI
Yang, Juan; Gong, Jiaxin; Wu, Longyu; Shu, Ji Limiting behavior of center manifolds for stochastic evolutionary equations with delay in varying phase spaces. (English) Zbl 1511.37092 J. Math. Phys. 64, No. 1, Article ID 012703, 34 p. (2023). MSC: 37L10 37L55 60H15 35R60 PDFBibTeX XMLCite \textit{J. Yang} et al., J. Math. Phys. 64, No. 1, Article ID 012703, 34 p. (2023; Zbl 1511.37092) Full Text: DOI
Chekroun, Mickaël D.; Liu, Honghu; McWilliams, James C.; Wang, Shouhong Transitions in stochastic non-equilibrium systems: efficient reduction and analysis. (English) Zbl 1518.60055 J. Differ. Equations 346, 145-204 (2023). MSC: 60H15 35R60 60H10 76M35 PDFBibTeX XMLCite \textit{M. D. Chekroun} et al., J. Differ. Equations 346, 145--204 (2023; Zbl 1518.60055) Full Text: DOI arXiv
Shi, Lin Singular limit of mean-square invariant unstable manifolds for SPDEs driven by nonlinear multiplicative white noise in varying phase spaces. (English) Zbl 1504.37068 Proc. Am. Math. Soc. 150, No. 10, 4407-4419 (2022). Reviewer: Anhui Gu (Chongqing) MSC: 37H30 37L55 60H15 35R60 PDFBibTeX XMLCite \textit{L. Shi}, Proc. Am. Math. Soc. 150, No. 10, 4407--4419 (2022; Zbl 1504.37068) Full Text: DOI
Shi, Lin; Zhou, Linfeng \(C^{1, \nu }\)-convergence of center manifolds for stochastic PDEs driven by colored noise on thin domain. (English) Zbl 1487.37070 J. Differ. Equations 310, 99-137 (2022). MSC: 37H30 60H15 35R60 PDFBibTeX XMLCite \textit{L. Shi} and \textit{L. Zhou}, J. Differ. Equations 310, 99--137 (2022; Zbl 1487.37070) Full Text: DOI
Zhao, Junyilang; Shen, Jun; Wang, Xiaohu Stationary approximations of inertial manifolds for stochastic retarded semilinear parabolic equations. (English) Zbl 1490.60193 J. Math. Anal. Appl. 506, No. 2, Article ID 125668, 34 p. (2022). Reviewer: Feng-Yu Wang (Tianjin) MSC: 60H15 37H10 34C28 60H40 PDFBibTeX XMLCite \textit{J. Zhao} et al., J. Math. Anal. Appl. 506, No. 2, Article ID 125668, 34 p. (2022; Zbl 1490.60193) Full Text: DOI
Shi, Lin; Li, Dingshi; Lu, Kening Limiting behavior of unstable manifolds for SPDEs in varying phase spaces. (English) Zbl 1484.37091 Discrete Contin. Dyn. Syst., Ser. B 26, No. 12, 6311-6337 (2021). MSC: 37L55 37L15 37L25 35R60 60H15 PDFBibTeX XMLCite \textit{L. Shi} et al., Discrete Contin. Dyn. Syst., Ser. B 26, No. 12, 6311--6337 (2021; Zbl 1484.37091) Full Text: DOI
Mohammed, Wael W. Fast-diffusion limit for reaction-diffusion equations with degenerate multiplicative and additive noise. (English) Zbl 1469.60193 J. Dyn. Differ. Equations 33, No. 1, 577-592 (2021). MSC: 60H10 60H15 35R60 PDFBibTeX XMLCite \textit{W. W. Mohammed}, J. Dyn. Differ. Equations 33, No. 1, 577--592 (2021; Zbl 1469.60193) Full Text: DOI
Shen, Jun; Lu, Kening; Zhang, Weinian Smoothness of invariant manifolds and foliations for infinite dimensional random dynamical systems. (English) Zbl 1450.37070 Sci. China, Math. 63, No. 9, 1877-1912 (2020). MSC: 37L55 37L10 37H30 37D25 37D10 57R30 PDFBibTeX XMLCite \textit{J. Shen} et al., Sci. China, Math. 63, No. 9, 1877--1912 (2020; Zbl 1450.37070) Full Text: DOI
Shi, Lin Smooth convergence of random center manifolds for SPDEs in varying phase spaces. (English) Zbl 1443.37040 J. Differ. Equations 269, No. 3, 1963-2011 (2020). MSC: 37H30 35R60 35B25 60H15 PDFBibTeX XMLCite \textit{L. Shi}, J. Differ. Equations 269, No. 3, 1963--2011 (2020; Zbl 1443.37040) Full Text: DOI
Chen, Xiaopeng; Roberts, Anthony J.; Duan, Jinqiao Centre manifolds for infinite dimensional random dynamical systems. (English) Zbl 1415.37098 Dyn. Syst. 34, No. 2, 334-355 (2019). MSC: 37L55 37D10 34D35 37H15 60H15 PDFBibTeX XMLCite \textit{X. Chen} et al., Dyn. Syst. 34, No. 2, 334--355 (2019; Zbl 1415.37098) Full Text: DOI arXiv
Chen, Xiaopeng; Roberts, Anthony; Duan, Jinqiao Centre manifolds for stochastic evolution equations. (English) Zbl 1325.60103 J. Difference Equ. Appl. 21, No. 7, 606-632 (2015). MSC: 60H15 35R60 37D10 34D35 PDFBibTeX XMLCite \textit{X. Chen} et al., J. Difference Equ. Appl. 21, No. 7, 606--632 (2015; Zbl 1325.60103) Full Text: DOI arXiv
Li, Ji; Lu, Kening; Bates, Peter Normally hyperbolic invariant manifolds for random dynamical systems. I: Persistence. (English) Zbl 1291.37093 Trans. Am. Math. Soc. 365, No. 11, 5933-5966 (2013). Reviewer: Helder Vilarinho (Covilhã) MSC: 37H10 34F05 34C45 37D10 37D05 PDFBibTeX XMLCite \textit{J. Li} et al., Trans. Am. Math. Soc. 365, No. 11, 5933--5966 (2013; Zbl 1291.37093) Full Text: DOI
Liu, Zhenxin Stochastic inertial manifolds for damped wave equations. (English) Zbl 1201.60065 Stoch. Dyn. 10, No. 2, 211-230 (2010). Reviewer: Carles Rovira (Barcelona) MSC: 60H15 35L70 35L25 35L55 37L25 37L55 PDFBibTeX XMLCite \textit{Z. Liu}, Stoch. Dyn. 10, No. 2, 211--230 (2010; Zbl 1201.60065) Full Text: DOI arXiv
Garrido-Atienza, María J.; Lu, Kening; Schmalfuß, Björn Unstable invariant manifolds for stochastic PDEs driven by a fractional Brownian motion. (English) Zbl 1186.37094 J. Differ. Equations 248, No. 7, 1637-1667 (2010). MSC: 37L55 60H15 37L25 35R60 60J65 PDFBibTeX XMLCite \textit{M. J. Garrido-Atienza} et al., J. Differ. Equations 248, No. 7, 1637--1667 (2010; Zbl 1186.37094) Full Text: DOI
Lu, Kening; Schmalfuß, Björn Invariant foliations for stochastic partial differential equations. (English) Zbl 1153.60362 Stoch. Dyn. 8, No. 3, 505-518 (2008). MSC: 60H15 37H10 37L55 37L25 37D10 PDFBibTeX XMLCite \textit{K. Lu} and \textit{B. Schmalfuß}, Stoch. Dyn. 8, No. 3, 505--518 (2008; Zbl 1153.60362) Full Text: DOI
Schmalfuss, Björn; Schneider, Klaus R. Invariant manifolds for random dynamical systems with slow and fast variables. (English) Zbl 1138.37032 J. Dyn. Differ. Equations 20, No. 1, 133-164 (2008). Reviewer: Hans Crauel (Frankfurt) MSC: 37H99 34F05 34C25 37D10 70K70 PDFBibTeX XMLCite \textit{B. Schmalfuss} and \textit{K. R. Schneider}, J. Dyn. Differ. Equations 20, No. 1, 133--164 (2008; Zbl 1138.37032) Full Text: DOI
Lu, Kening; Schmalfuß, Björn Invariant manifolds for stochastic wave equations. (English) Zbl 1113.37056 J. Differ. Equations 236, No. 2, 460-492 (2007). MSC: 37L55 35R60 60H15 PDFBibTeX XMLCite \textit{K. Lu} and \textit{B. Schmalfuß}, J. Differ. Equations 236, No. 2, 460--492 (2007; Zbl 1113.37056) Full Text: DOI
Caraballo, Tomás; Crauel, Hans; Langa, José A.; Robinson, James C. The effect of noise on the Chafee-Infante equation: a nonlinear case study. (English) Zbl 1173.60022 Proc. Am. Math. Soc. 135, No. 2, 373-382 (2007). MSC: 60H15 35K20 35K55 35R60 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Proc. Am. Math. Soc. 135, No. 2, 373--382 (2007; Zbl 1173.60022) Full Text: DOI
Bakhtin, Yuri; Mattingly, Jonathan C. Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations. (English) Zbl 1098.34063 Commun. Contemp. Math. 7, No. 5, 553-582 (2005). Reviewer: Vigirdas Mackevičius (Vilnius) MSC: 34K50 35Q30 35R60 37H10 60H15 60H10 76D05 76M35 PDFBibTeX XMLCite \textit{Y. Bakhtin} and \textit{J. C. Mattingly}, Commun. Contemp. Math. 7, No. 5, 553--582 (2005; Zbl 1098.34063) Full Text: DOI arXiv
Duan, Jinqiao; Lu, Kening; Schmalfuss, Björn Invariant manifolds for stochastic partial differential equations. (English) Zbl 1052.60048 Ann. Probab. 31, No. 4, 2109-2135 (2003). Reviewer: Katarina Janková (Bratislava) MSC: 60H15 37H10 37L55 37D10 PDFBibTeX XMLCite \textit{J. Duan} et al., Ann. Probab. 31, No. 4, 2109--2135 (2003; Zbl 1052.60048) Full Text: DOI arXiv Euclid