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Meshless method for the stationary incompressible Navier-Stokes equations
The stochastic Landau equation as an amplitude equation
1. | Institut für Mathematik, RWTH Aachen, D-52062 Aachen, Germany, Germany |
2. | Mathematisches Institute, Universität Bayreuth, D-95440 Bayreuth, Germany |
[1] |
Ling-Jun Wang. The dynamics of small amplitude solutions of the Swift-Hohenberg equation on a large interval. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1129-1156. doi: 10.3934/cpaa.2012.11.1129 |
[2] |
Yanfeng Guo, Jinqiao Duan, Donglong Li. Approximation of random invariant manifolds for a stochastic Swift-Hohenberg equation. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 1701-1715. doi: 10.3934/dcdss.2016071 |
[3] |
J. Burke, Edgar Knobloch. Multipulse states in the Swift-Hohenberg equation. Conference Publications, 2009, 2009 (Special) : 109-117. doi: 10.3934/proc.2009.2009.109 |
[4] |
Jongmin Han, Masoud Yari. Dynamic bifurcation of the complex Swift-Hohenberg equation. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 875-891. doi: 10.3934/dcdsb.2009.11.875 |
[5] |
Peng Gao. Averaging principles for the Swift-Hohenberg equation. Communications on Pure and Applied Analysis, 2020, 19 (1) : 293-310. doi: 10.3934/cpaa.2020016 |
[6] |
Yuncherl Choi, Taeyoung Ha, Jongmin Han, Doo Seok Lee. Bifurcation and final patterns of a modified Swift-Hohenberg equation. Discrete and Continuous Dynamical Systems - B, 2017, 22 (7) : 2543-2567. doi: 10.3934/dcdsb.2017087 |
[7] |
Yixia Shi, Maoan Han. Existence of generalized homoclinic solutions for a modified Swift-Hohenberg equation. Discrete and Continuous Dynamical Systems - S, 2020, 13 (11) : 3189-3204. doi: 10.3934/dcdss.2020114 |
[8] |
Shengfu Deng. Periodic solutions and homoclinic solutions for a Swift-Hohenberg equation with dispersion. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 1647-1662. doi: 10.3934/dcdss.2016068 |
[9] |
John Burke, Edgar Knobloch. Normal form for spatial dynamics in the Swift-Hohenberg equation. Conference Publications, 2007, 2007 (Special) : 170-180. doi: 10.3934/proc.2007.2007.170 |
[10] |
Toshiyuki Ogawa, Takashi Okuda. Bifurcation analysis to Swift-Hohenberg equation with Steklov type boundary conditions. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 273-297. doi: 10.3934/dcds.2009.25.273 |
[11] |
Kevin Li. Dynamic transitions of the Swift-Hohenberg equation with third-order dispersion. Discrete and Continuous Dynamical Systems - B, 2021, 26 (12) : 6069-6090. doi: 10.3934/dcdsb.2021003 |
[12] |
Jongmin Han, Chun-Hsiung Hsia. Dynamical bifurcation of the two dimensional Swift-Hohenberg equation with odd periodic condition. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2431-2449. doi: 10.3934/dcdsb.2012.17.2431 |
[13] |
Andrea Giorgini. On the Swift-Hohenberg equation with slow and fast dynamics: well-posedness and long-time behavior. Communications on Pure and Applied Analysis, 2016, 15 (1) : 219-241. doi: 10.3934/cpaa.2016.15.219 |
[14] |
Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations and Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013 |
[15] |
Masoud Yari. Attractor bifurcation and final patterns of the n-dimensional and generalized Swift-Hohenberg equations. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 441-456. doi: 10.3934/dcdsb.2007.7.441 |
[16] |
Evelyne Miot, Mario Pulvirenti, Chiara Saffirio. On the Kac model for the Landau equation. Kinetic and Related Models, 2011, 4 (1) : 333-344. doi: 10.3934/krm.2011.4.333 |
[17] |
Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control and Related Fields, 2016, 6 (4) : 595-628. doi: 10.3934/mcrf.2016017 |
[18] |
Sebastián Ferrer, Martin Lara. Families of canonical transformations by Hamilton-Jacobi-Poincaré equation. Application to rotational and orbital motion. Journal of Geometric Mechanics, 2010, 2 (3) : 223-241. doi: 10.3934/jgm.2010.2.223 |
[19] |
Manuel de León, Juan Carlos Marrero, David Martín de Diego. Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics. Journal of Geometric Mechanics, 2010, 2 (2) : 159-198. doi: 10.3934/jgm.2010.2.159 |
[20] |
Thierry Horsin, Peter I. Kogut. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. I. Existence result. Mathematical Control and Related Fields, 2015, 5 (1) : 73-96. doi: 10.3934/mcrf.2015.5.73 |
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