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A domain decomposition method for a two-scale transport equation with energy flux conserved at the interface
Self-averaging of kinetic models for waves in random media
1. | Department of Applied Physics and Applied Mathematics, Columbia University, New York NY, 10027 |
2. | Université de Lyon, Université Lyon 1, CNRS, UMR 5208 Institut Camille Jordan/ISTIL, Bâtiment du Doyen Jean Braconnier, 43, blvd du 11 novembre 1918, F - 69622 Villeurbanne Cedex, France |
[1] |
Reika Fukuizumi. Stability and instability of standing waves for the nonlinear Schrödinger equation with harmonic potential. Discrete and Continuous Dynamical Systems, 2001, 7 (3) : 525-544. doi: 10.3934/dcds.2001.7.525 |
[2] |
François Genoud. Existence and stability of high frequency standing waves for a nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1229-1247. doi: 10.3934/dcds.2009.25.1229 |
[3] |
Sevdzhan Hakkaev. Orbital stability of solitary waves of the Schrödinger-Boussinesq equation. Communications on Pure and Applied Analysis, 2007, 6 (4) : 1043-1050. doi: 10.3934/cpaa.2007.6.1043 |
[4] |
Stephen Coombes, Helmut Schmidt, Carlo R. Laing, Nils Svanstedt, John A. Wyller. Waves in random neural media. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 2951-2970. doi: 10.3934/dcds.2012.32.2951 |
[5] |
Naoufel Ben Abdallah, Yongyong Cai, Francois Castella, Florian Méhats. Second order averaging for the nonlinear Schrödinger equation with strongly anisotropic potential. Kinetic and Related Models, 2011, 4 (4) : 831-856. doi: 10.3934/krm.2011.4.831 |
[6] |
Wolfgang Wagner. A random cloud model for the Schrödinger equation. Kinetic and Related Models, 2014, 7 (2) : 361-379. doi: 10.3934/krm.2014.7.361 |
[7] |
Peng Gao, Yong Li. Averaging principle for the Schrödinger equations†. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2147-2168. doi: 10.3934/dcdsb.2017089 |
[8] |
Alex H. Ardila. Stability of standing waves for a nonlinear SchrÖdinger equation under an external magnetic field. Communications on Pure and Applied Analysis, 2018, 17 (1) : 163-175. doi: 10.3934/cpaa.2018010 |
[9] |
Reika Fukuizumi, Louis Jeanjean. Stability of standing waves for a nonlinear Schrödinger equation wdelta potentialith a repulsive Dirac. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 121-136. doi: 10.3934/dcds.2008.21.121 |
[10] |
Jun-ichi Segata. Initial value problem for the fourth order nonlinear Schrödinger type equation on torus and orbital stability of standing waves. Communications on Pure and Applied Analysis, 2015, 14 (3) : 843-859. doi: 10.3934/cpaa.2015.14.843 |
[11] |
Guillaume Bal, Tomasz Komorowski, Lenya Ryzhik. Kinetic limits for waves in a random medium. Kinetic and Related Models, 2010, 3 (4) : 529-644. doi: 10.3934/krm.2010.3.529 |
[12] |
Fábio Natali, Ademir Pastor. Orbital stability of periodic waves for the Klein-Gordon-Schrödinger system. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 221-238. doi: 10.3934/dcds.2011.31.221 |
[13] |
Santosh Bhattarai. Stability of normalized solitary waves for three coupled nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 1789-1811. doi: 10.3934/dcds.2016.36.1789 |
[14] |
François Genoud, Charles A. Stuart. Schrödinger equations with a spatially decaying nonlinearity: Existence and stability of standing waves. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 137-186. doi: 10.3934/dcds.2008.21.137 |
[15] |
Alexander Komech, Elena Kopylova, David Stuart. On asymptotic stability of solitons in a nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1063-1079. doi: 10.3934/cpaa.2012.11.1063 |
[16] |
Hiroyuki Hirayama, Mamoru Okamoto. Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 6943-6974. doi: 10.3934/dcds.2016102 |
[17] |
Yue Liu. Existence of unstable standing waves for the inhomogeneous nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2008, 7 (1) : 193-209. doi: 10.3934/cpaa.2008.7.193 |
[18] |
Guillaume Bal, Lenya Ryzhik. Stability of time reversed waves in changing media. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 793-815. doi: 10.3934/dcds.2005.12.793 |
[19] |
Martial Agueh, Guillaume Carlier, Reinhard Illner. Remarks on a class of kinetic models of granular media: Asymptotics and entropy bounds. Kinetic and Related Models, 2015, 8 (2) : 201-214. doi: 10.3934/krm.2015.8.201 |
[20] |
Tzong-Yow Lee and Fred Torcaso. Wave propagation in a lattice KPP equation in random media. Electronic Research Announcements, 1997, 3: 121-125. |
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