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Singular perturbation systems with stochastic forcing and the renormalization group method
1.  Department of Mathematics and The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, United States 
2.  Department of Mathematics, University of Southern California, Los Angeles, CA 90089 
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Yanzhao Cao, Li Yin. Spectral Galerkin method for stochastic wave equations driven by spacetime white noise. Communications on Pure & Applied Analysis, 2007, 6 (3) : 607617. doi: 10.3934/cpaa.2007.6.607 
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Wenlei Li, Shaoyun Shi. Singular perturbed renormalization group theory and its application to highly oscillatory problems. Discrete & Continuous Dynamical Systems  B, 2018, 23 (4) : 18191833. doi: 10.3934/dcdsb.2018089 
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Yan Wang, Lei Wang, Yanxiang Zhao, Aimin Song, Yanping Ma. A stochastic model for microbial fermentation process under Gaussian white noise environment. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 381392. doi: 10.3934/naco.2015.5.381 
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Boris P. Belinskiy, Peter Caithamer. Stochastic stability of some mechanical systems with a multiplicative white noise. Conference Publications, 2003, 2003 (Special) : 9199. doi: 10.3934/proc.2003.2003.91 
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Shang Wu, Pengfei Xu, Jianhua Huang, Wei Yan. Ergodicity of stochastic damped Ostrovsky equation driven by white noise. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020175 
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I. Moise, Roger Temam. Renormalization group method: Application to NavierStokes equation. Discrete & Continuous Dynamical Systems  A, 2000, 6 (1) : 191210. doi: 10.3934/dcds.2000.6.191 
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Ilona Gucwa, Peter Szmolyan. Geometric singular perturbation analysis of an autocatalator model. Discrete & Continuous Dynamical Systems  S, 2009, 2 (4) : 783806. doi: 10.3934/dcdss.2009.2.783 
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Shengfan Zhou, Min Zhao. Fractal dimension of random attractor for stochastic nonautonomous damped wave equation with linear multiplicative white noise. Discrete & Continuous Dynamical Systems  A, 2016, 36 (5) : 28872914. doi: 10.3934/dcds.2016.36.2887 
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Tianlong Shen, Jianhua Huang, Caibin Zeng. Time fractional and space nonlocal stochastic boussinesq equations driven by gaussian white noise. Discrete & Continuous Dynamical Systems  B, 2018, 23 (4) : 15231533. doi: 10.3934/dcdsb.2018056 
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Ying Hu, Shanjian Tang. Nonlinear backward stochastic evolutionary equations driven by a spacetime white noise. Mathematical Control & Related Fields, 2018, 8 (3&4) : 739751. doi: 10.3934/mcrf.2018032 
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Xingni Tan, Fuqi Yin, Guihong Fan. Random exponential attractor for stochastic discrete long waveshort wave resonance equation with multiplicative white noise. Discrete & Continuous Dynamical Systems  B, 2020, 25 (8) : 31533170. doi: 10.3934/dcdsb.2020055 
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Leonid Shaikhet. Stability of delay differential equations with fading stochastic perturbations of the type of white noise and poisson's jumps. Discrete & Continuous Dynamical Systems  B, 2020, 25 (9) : 36513657. doi: 10.3934/dcdsb.2020077 
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G. A. Braga, Frederico Furtado, Jussara M. Moreira, Leonardo T. Rolla. Renormalization group analysis of nonlinear diffusion equations with time dependent coefficients: Analytical results. Discrete & Continuous Dynamical Systems  B, 2007, 7 (4) : 699715. doi: 10.3934/dcdsb.2007.7.699 
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Xinfu Chen, Carey Caginalp, Jianghao Hao, Yajing Zhang. Effects of white noise in multistable dynamics. Discrete & Continuous Dynamical Systems  B, 2013, 18 (7) : 18051825. doi: 10.3934/dcdsb.2013.18.1805 
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Zhaojuan Wang, Shengfan Zhou. Random attractor and random exponential attractor for stochastic nonautonomous damped cubic wave equation with linear multiplicative white noise. Discrete & Continuous Dynamical Systems  A, 2018, 38 (9) : 47674817. doi: 10.3934/dcds.2018210 
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SzeBi Hsu, Bernold Fiedler, HsiuHau Lin. Classification of potential flows under renormalization group transformation. Discrete & Continuous Dynamical Systems  B, 2016, 21 (2) : 437446. doi: 10.3934/dcdsb.2016.21.437 
[20] 
Zainidin Eshkuvatov. Homotopy perturbation method and Chebyshev polynomials for solving a class of singular and hypersingular integral equations. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 337350. doi: 10.3934/naco.2018022 
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