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Homogenization and correctors for the wave equation in non periodic perforated domains
1. | Laboratoire de Mathématiques Raphaël Salem, UMR CNRS 6085, Avenue de l’Université, BP 12, 76801 Saint Etienne de Rouvray, France |
2. | Laboratoire Jacques-Louis Lions, UMR CNRS 7598, Université Paris 6 BP 187, 4 Place Jussieu 75252 Paris Cedex 05, France |
[1] |
Andriy Bondarenko, Guy Bouchitté, Luísa Mascarenhas, Rajesh Mahadevan. Rate of convergence for correctors in almost periodic homogenization. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 503-514. doi: 10.3934/dcds.2005.13.503 |
[2] |
Vo Anh Khoa, Thi Kim Thoa Thieu, Ekeoma Rowland Ijioma. On a pore-scale stationary diffusion equation: Scaling effects and correctors for the homogenization limit. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2451-2477. doi: 10.3934/dcdsb.2020190 |
[3] |
Zhanying Yang. Homogenization and correctors for the hyperbolic problems with imperfect interfaces via the periodic unfolding method. Communications on Pure and Applied Analysis, 2014, 13 (1) : 249-272. doi: 10.3934/cpaa.2014.13.249 |
[4] |
G. Gentile, V. Mastropietro. Convergence of Lindstedt series for the non linear wave equation. Communications on Pure and Applied Analysis, 2004, 3 (3) : 509-514. doi: 10.3934/cpaa.2004.3.509 |
[5] |
M. M. Cavalcanti, V.N. Domingos Cavalcanti, D. Andrade, T. F. Ma. Homogenization for a nonlinear wave equation in domains with holes of small capacity. Discrete and Continuous Dynamical Systems, 2006, 16 (4) : 721-743. doi: 10.3934/dcds.2006.16.721 |
[6] |
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 |
[7] |
Kenji Nakanishi. Modified wave operators for the Hartree equation with data, image and convergence in the same space. Communications on Pure and Applied Analysis, 2002, 1 (2) : 237-252. doi: 10.3934/cpaa.2002.1.237 |
[8] |
Takiko Sasaki. Convergence of a blow-up curve for a semilinear wave equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 1133-1143. doi: 10.3934/dcdss.2020388 |
[9] |
Hongyong Cui, Peter E. Kloeden, Wenqiang Zhao. Strong $ (L^2,L^\gamma\cap H_0^1) $-continuity in initial data of nonlinear reaction-diffusion equation in any space dimension. Electronic Research Archive, 2020, 28 (3) : 1357-1374. doi: 10.3934/era.2020072 |
[10] |
Martin Gugat, Günter Leugering, Ke Wang. Neumann boundary feedback stabilization for a nonlinear wave equation: A strict $H^2$-lyapunov function. Mathematical Control and Related Fields, 2017, 7 (3) : 419-448. doi: 10.3934/mcrf.2017015 |
[11] |
Jean Louis Woukeng. $\sum $-convergence and reiterated homogenization of nonlinear parabolic operators. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1753-1789. doi: 10.3934/cpaa.2010.9.1753 |
[12] |
Jie Zhao. Convergence rates for elliptic reiterated homogenization problems. Communications on Pure and Applied Analysis, 2013, 12 (6) : 2787-2795. doi: 10.3934/cpaa.2013.12.2787 |
[13] |
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 |
[14] |
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 |
[15] |
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 |
[16] |
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 |
[17] |
Jussi Korpela, Matti Lassas, Lauri Oksanen. Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation. Inverse Problems and Imaging, 2019, 13 (3) : 575-596. doi: 10.3934/ipi.2019027 |
[18] |
Ioana Ciotir, Nicolas Forcadel, Wilfredo Salazar. Homogenization of a stochastic viscous transport equation. Evolution Equations and Control Theory, 2021, 10 (2) : 353-364. doi: 10.3934/eect.2020070 |
[19] |
Weisheng Niu, Yao Xu. Convergence rates in homogenization of higher-order parabolic systems. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 4203-4229. doi: 10.3934/dcds.2018183 |
[20] |
Fabio Camilli, Claudio Marchi. On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems. Networks and Heterogeneous Media, 2011, 6 (1) : 61-75. doi: 10.3934/nhm.2011.6.61 |
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