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Multiscale numerical method for nonlinear Maxwell equations
1.  Mathématiques Appliquées de Bordeaux, Université Bordeaux 1 et CNRS UMR 5466, 351 cours de la Libération, 33405 Talence cedex, France, France 
[1] 
W. Wei, H. M. Yin. Global solvability for a singular nonlinear Maxwell's equations. Communications on Pure & Applied Analysis, 2005, 4 (2) : 431444. doi: 10.3934/cpaa.2005.4.431 
[2] 
Björn Birnir, Niklas Wellander. Homogenized Maxwell's equations; A model for ceramic varistors. Discrete & Continuous Dynamical Systems  B, 2006, 6 (2) : 257272. doi: 10.3934/dcdsb.2006.6.257 
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Gang Bao. Mathematical modeling of nonlinear diffracvtive optics. Conference Publications, 1998, 1998 (Special) : 8999. doi: 10.3934/proc.1998.1998.89 
[4] 
M. Eller. On boundary regularity of solutions to Maxwell's equations with a homogeneous conservative boundary condition. Discrete & Continuous Dynamical Systems  S, 2009, 2 (3) : 473481. doi: 10.3934/dcdss.2009.2.473 
[5] 
Oleg Yu. Imanuvilov, Masahiro Yamamoto. Calderón problem for Maxwell's equations in cylindrical domain. Inverse Problems & Imaging, 2014, 8 (4) : 11171137. doi: 10.3934/ipi.2014.8.1117 
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B. L. G. Jonsson. Wave splitting of Maxwell's equations with anisotropic heterogeneous constitutive relations. Inverse Problems & Imaging, 2009, 3 (3) : 405452. doi: 10.3934/ipi.2009.3.405 
[7] 
Andreas Kirsch. An integral equation approach and the interior transmission problem for Maxwell's equations. Inverse Problems & Imaging, 2007, 1 (1) : 159179. doi: 10.3934/ipi.2007.1.159 
[8] 
Cleverson R. da Luz, Gustavo Alberto Perla Menzala. Uniform stabilization of anisotropic Maxwell's equations with boundary dissipation. Discrete & Continuous Dynamical Systems  S, 2009, 2 (3) : 547558. doi: 10.3934/dcdss.2009.2.547 
[9] 
Gang Bao, Bin Hu, Peijun Li, Jue Wang. Analysis of timedomain Maxwell's equations in biperiodic structures. Discrete & Continuous Dynamical Systems  B, 2020, 25 (1) : 259286. doi: 10.3934/dcdsb.2019181 
[10] 
Daomin Cao, Ezzat S. Noussair, Shusen Yan. On the profile of solutions for an elliptic problem arising in nonlinear optics. Discrete & Continuous Dynamical Systems  A, 2004, 11 (2&3) : 649666. doi: 10.3934/dcds.2004.11.649 
[11] 
Dirk Pauly. On Maxwell's and Poincaré's constants. Discrete & Continuous Dynamical Systems  S, 2015, 8 (3) : 607618. doi: 10.3934/dcdss.2015.8.607 
[12] 
Kim Dang Phung. Energy decay for Maxwell's equations with Ohm's law in partially cubic domains. Communications on Pure & Applied Analysis, 2013, 12 (5) : 22292266. doi: 10.3934/cpaa.2013.12.2229 
[13] 
J. J. Morgan, HongMing Yin. On Maxwell's system with a thermal effect. Discrete & Continuous Dynamical Systems  B, 2001, 1 (4) : 485494. doi: 10.3934/dcdsb.2001.1.485 
[14] 
Cheng Hou Tsang, Boris A. Malomed, Kwok Wing Chow. Exact solutions for periodic and solitary matter waves in nonlinear lattices. Discrete & Continuous Dynamical Systems  S, 2011, 4 (5) : 12991325. doi: 10.3934/dcdss.2011.4.1299 
[15] 
S. S. Krigman. Exact boundary controllability of Maxwell's equations with weak conductivity in the heterogeneous medium inside a general domain. Conference Publications, 2007, 2007 (Special) : 590601. doi: 10.3934/proc.2007.2007.590 
[16] 
Dina Kalinichenko, Volker Reitmann, Sergey Skopinov. Asymptotic behavior of solutions to a coupled system of Maxwell's equations and a controlled differential inclusion. Conference Publications, 2013, 2013 (special) : 407414. doi: 10.3934/proc.2013.2013.407 
[17] 
Remi Sentis. Models and simulations for the laserplasma interaction and the threewave coupling problem. Discrete & Continuous Dynamical Systems  S, 2012, 5 (2) : 329343. doi: 10.3934/dcdss.2012.5.329 
[18] 
Tian Ma, Shouhong Wang. Gravitational Field Equations and Theory of Dark Matter and Dark Energy. Discrete & Continuous Dynamical Systems  A, 2014, 34 (2) : 335366. doi: 10.3934/dcds.2014.34.335 
[19] 
JiannSheng Jiang, ChiKun Lin, ChiHua Liu. Homogenization of the Maxwell's system for conducting media. Discrete & Continuous Dynamical Systems  B, 2008, 10 (1) : 91107. doi: 10.3934/dcdsb.2008.10.91 
[20] 
Shuangqian Liu, Qinghua Xiao. The relativistic VlasovMaxwellBoltzmann system for short range interaction. Kinetic & Related Models, 2016, 9 (3) : 515550. doi: 10.3934/krm.2016005 
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