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Stochastic Galerkin method for elliptic spdes: A white noise approach
1.  Worcester Polytechnic Institute, Department of Mathematical Sciences, 100 Institute Rd, Worcester, MA 016092280, United States, United States 
[1] 
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 
[2] 
Kexue Li, Jigen Peng, Junxiong Jia. Explosive solutions of parabolic stochastic partial differential equations with lévy noise. Discrete & Continuous Dynamical Systems  A, 2017, 37 (10) : 51055125. doi: 10.3934/dcds.2017221 
[3] 
Arnulf Jentzen. Taylor expansions of solutions of stochastic partial differential equations. Discrete & Continuous Dynamical Systems  B, 2010, 14 (2) : 515557. doi: 10.3934/dcdsb.2010.14.515 
[4] 
Yanqing Wang. A semidiscrete Galerkin scheme for backward stochastic parabolic differential equations. Mathematical Control & Related Fields, 2016, 6 (3) : 489515. doi: 10.3934/mcrf.2016013 
[5] 
Can Huang, Zhimin Zhang. The spectral collocation method for stochastic differential equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (3) : 667679. doi: 10.3934/dcdsb.2013.18.667 
[6] 
David Lipshutz. Exit time asymptotics for small noise stochastic delay differential equations. Discrete & Continuous Dynamical Systems  A, 2018, 38 (6) : 30993138. doi: 10.3934/dcds.2018135 
[7] 
Zhen Li, Jicheng Liu. Synchronization for stochastic differential equations with nonlinear multiplicative noise in the mean square sense. Discrete & Continuous Dynamical Systems  B, 2019, 24 (10) : 57095736. doi: 10.3934/dcdsb.2019103 
[8] 
Tomás Caraballo, José Real, T. Taniguchi. The exponential stability of neutral stochastic delay partial differential equations. Discrete & Continuous Dynamical Systems  A, 2007, 18 (2&3) : 295313. doi: 10.3934/dcds.2007.18.295 
[9] 
Zhongkai Guo. Invariant foliations for stochastic partial differential equations with dynamic boundary conditions. Discrete & Continuous Dynamical Systems  A, 2015, 35 (11) : 52035219. doi: 10.3934/dcds.2015.35.5203 
[10] 
Mogtaba Mohammed, Mamadou Sango. Homogenization of nonlinear hyperbolic stochastic partial differential equations with nonlinear damping and forcing. Networks & Heterogeneous Media, 2019, 14 (2) : 341369. doi: 10.3934/nhm.2019014 
[11] 
Sergio Albeverio, Sonia Mazzucchi. Infinite dimensional integrals and partial differential equations for stochastic and quantum phenomena. Journal of Geometric Mechanics, 2019, 11 (2) : 123137. doi: 10.3934/jgm.2019006 
[12] 
Minoo Kamrani. Numerical solution of partial differential equations with stochastic Neumann boundary conditions. Discrete & Continuous Dynamical Systems  B, 2019, 24 (10) : 53375354. doi: 10.3934/dcdsb.2019061 
[13] 
Xin Yu, Guojie Zheng, Chao Xu. The $C$regularized semigroup method for partial differential equations with delays. Discrete & Continuous Dynamical Systems  A, 2016, 36 (9) : 51635181. doi: 10.3934/dcds.2016024 
[14] 
Ali Hamidoǧlu. On general form of the Tanh method and its application to nonlinear partial differential equations. Numerical Algebra, Control & Optimization, 2016, 6 (2) : 175181. doi: 10.3934/naco.2016007 
[15] 
Ludwig Arnold, Igor Chueshov. Cooperative random and stochastic differential equations. Discrete & Continuous Dynamical Systems  A, 2001, 7 (1) : 133. doi: 10.3934/dcds.2001.7.1 
[16] 
Herbert Koch. Partial differential equations with nonEuclidean geometries. Discrete & Continuous Dynamical Systems  S, 2008, 1 (3) : 481504. doi: 10.3934/dcdss.2008.1.481 
[17] 
Wilhelm Schlag. Spectral theory and nonlinear partial differential equations: A survey. Discrete & Continuous Dynamical Systems  A, 2006, 15 (3) : 703723. doi: 10.3934/dcds.2006.15.703 
[18] 
Eugenia N. Petropoulou, Panayiotis D. Siafarikas. Polynomial solutions of linear partial differential equations. Communications on Pure & Applied Analysis, 2009, 8 (3) : 10531065. doi: 10.3934/cpaa.2009.8.1053 
[19] 
Nguyen Thieu Huy, Ngo Quy Dang. Dichotomy and periodic solutions to partial functional differential equations. Discrete & Continuous Dynamical Systems  B, 2017, 22 (8) : 31273144. doi: 10.3934/dcdsb.2017167 
[20] 
Barbara AbrahamShrauner. Exact solutions of nonlinear partial differential equations. Discrete & Continuous Dynamical Systems  S, 2018, 11 (4) : 577582. doi: 10.3934/dcdss.2018032 
2018 Impact Factor: 1.008
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