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Stochastic wave equations with cubic nonlinearity and Q-regular additive noise in $\mathbb{R}^2$
1. | Southern Illinois University, Department of Mathematics, MC 4408, 1245 Lincoln Drive, Carbondale, IL 62901-7316 |
[1] |
Henri Schurz. Analysis and discretization of semi-linear stochastic wave equations with cubic nonlinearity and additive space-time noise. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 353-363. doi: 10.3934/dcdss.2008.1.353 |
[2] |
Henri Schurz. Stochastic heat equations with cubic nonlinearity and additive space-time noise in 2D. Conference Publications, 2013, 2013 (special) : 673-684. doi: 10.3934/proc.2013.2013.673 |
[3] |
Yanzhao Cao, Li Yin. Spectral Galerkin method for stochastic wave equations driven by space-time white noise. Communications on Pure and Applied Analysis, 2007, 6 (3) : 607-617. doi: 10.3934/cpaa.2007.6.607 |
[4] |
Jae Gil Choi, David Skoug. Algebraic structure of the $ L_2 $ analytic Fourier–Feynman transform associated with Gaussian paths on Wiener space. Communications on Pure and Applied Analysis, 2020, 19 (7) : 3829-3842. doi: 10.3934/cpaa.2020169 |
[5] |
Ying Hu, Shanjian Tang. Nonlinear backward stochastic evolutionary equations driven by a space-time white noise. Mathematical Control and Related Fields, 2018, 8 (3&4) : 739-751. doi: 10.3934/mcrf.2018032 |
[6] |
Boris P. Belinskiy, Peter Caithamer. Energy estimate for the wave equation driven by a fractional Gaussian noise. Conference Publications, 2007, 2007 (Special) : 92-101. doi: 10.3934/proc.2007.2007.92 |
[7] |
Boris P. Belinskiy, Peter Caithamer. Energy of an elastic mechanical system driven by Gaussian noise white in time. Conference Publications, 2001, 2001 (Special) : 39-49. doi: 10.3934/proc.2001.2001.39 |
[8] |
Tianlong Shen, Jianhua Huang, Caibin Zeng. Time fractional and space nonlocal stochastic boussinesq equations driven by gaussian white noise. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1523-1533. doi: 10.3934/dcdsb.2018056 |
[9] |
Montgomery Taylor. The diffusion phenomenon for damped wave equations with space-time dependent coefficients. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 5921-5941. doi: 10.3934/dcds.2018257 |
[10] |
Adam Andersson, Felix Lindner. Malliavin regularity and weak approximation of semilinear SPDEs with Lévy noise. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4271-4294. doi: 10.3934/dcdsb.2019081 |
[11] |
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 and Optimization, 2015, 5 (4) : 381-392. doi: 10.3934/naco.2015.5.381 |
[12] |
Georgios T. Kossioris, Georgios E. Zouraris. Finite element approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise. Discrete and Continuous Dynamical Systems - B, 2013, 18 (7) : 1845-1872. doi: 10.3934/dcdsb.2013.18.1845 |
[13] |
Igor Kukavica. On Fourier parametrization of global attractors for equations in one space dimension. Discrete and Continuous Dynamical Systems, 2005, 13 (3) : 553-560. doi: 10.3934/dcds.2005.13.553 |
[14] |
Yuming Zhang. On continuity equations in space-time domains. Discrete and Continuous Dynamical Systems, 2018, 38 (10) : 4837-4873. doi: 10.3934/dcds.2018212 |
[15] |
María J. Garrido-Atienza, Bohdan Maslowski, Jana Šnupárková. Semilinear stochastic equations with bilinear fractional noise. Discrete and Continuous Dynamical Systems - B, 2016, 21 (9) : 3075-3094. doi: 10.3934/dcdsb.2016088 |
[16] |
C. M. Khalique, G. S. Pai. Conservation laws and invariant solutions for soil water equations. Conference Publications, 2003, 2003 (Special) : 477-481. doi: 10.3934/proc.2003.2003.477 |
[17] |
Kei Nakamura, Tohru Ozawa. Finite charge solutions to cubic Schrödinger equations with a nonlocal nonlinearity in one space dimension. Discrete and Continuous Dynamical Systems, 2013, 33 (2) : 789-801. doi: 10.3934/dcds.2013.33.789 |
[18] |
Kyouhei Wakasa. The lifespan of solutions to semilinear damped wave equations in one space dimension. Communications on Pure and Applied Analysis, 2016, 15 (4) : 1265-1283. doi: 10.3934/cpaa.2016.15.1265 |
[19] |
Ionuţ Munteanu. Design of boundary stabilizers for the non-autonomous cubic semilinear heat equation driven by a multiplicative noise. Evolution Equations and Control Theory, 2020, 9 (3) : 795-816. doi: 10.3934/eect.2020034 |
[20] |
Georges Bastin, B. Haut, Jean-Michel Coron, Brigitte d'Andréa-Novel. Lyapunov stability analysis of networks of scalar conservation laws. Networks and Heterogeneous Media, 2007, 2 (4) : 751-759. doi: 10.3934/nhm.2007.2.751 |
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