
Previous Article
A support theorem for the geodesic ray transform of symmetric tensor fields
 IPI Home
 This Issue

Next Article
Reciprocity gap music imaging for an inverse scattering problem in twolayered media
Wave splitting of Maxwell's equations with anisotropic heterogeneous constitutive relations
1.  Electromagnetic Engineering, School of Electrical Engineering, Royal Institute of Technology, SE100 44 Stockholm, Sweden 
In the process of defining the wavefield decomposition (wavesplitting), the resolvent set of the timeLaplace representation of the system's matrix is analyzed. This set is shown to contain a strip around the imaginary axis. We construct a splitting matrix as a DunfordTaylor type integral over the resolvent of the unbounded operator defined by the electromagnetic system's matrix. The splitting matrix commutes with the system's matrix and the decomposition is obtained via a generalized eigenvalueeigenvector procedure. The decomposition is expressed in terms of components of the splitting matrix. The constructive solution to the question of the existence of a decomposition also generates an impedance mapping solution to an algebraic Riccati operator equation. This solution is the electromagnetic generalization in an anisotropic media of a DirichlettoNeumann map.
[1] 
Shengxin Zhu, Tongxiang Gu, Xingping Liu. AIMS: Average information matrix splitting. Mathematical Foundations of Computing, 2020, 3 (4) : 301308. doi: 10.3934/mfc.2020012 
[2] 
Liu Rui. The explicit nonlinear wave solutions of the generalized $b$equation. Communications on Pure & Applied Analysis, 2013, 12 (2) : 10291047. doi: 10.3934/cpaa.2013.12.1029 
[3] 
Gengen Zhang. Time splitting combined with exponential wave integrator Fourier pseudospectral method for quantum Zakharov system. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021149 
[4] 
Weiguo Wang, Weichao Wang, Rencang Li. Deflating irreducible singular Mmatrix algebraic Riccati equations. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 491518. doi: 10.3934/naco.2013.3.491 
[5] 
Huijun He, Zhaoyang Yin. On the Cauchy problem for a generalized twocomponent shallow water wave system with fractional higherorder inertia operators. Discrete & Continuous Dynamical Systems, 2017, 37 (3) : 15091537. doi: 10.3934/dcds.2017062 
[6] 
Tatsien Li, Bopeng Rao, Yimin Wei. Generalized exact boundary synchronization for a coupled system of wave equations. Discrete & Continuous Dynamical Systems, 2014, 34 (7) : 28932905. doi: 10.3934/dcds.2014.34.2893 
[7] 
Bendong Lou. Traveling wave solutions of a generalized curvature flow equation in the plane. Conference Publications, 2007, 2007 (Special) : 687693. doi: 10.3934/proc.2007.2007.687 
[8] 
Stefan Possanner, Claudia Negulescu. Diffusion limit of a generalized matrix Boltzmann equation for spinpolarized transport. Kinetic & Related Models, 2011, 4 (4) : 11591191. doi: 10.3934/krm.2011.4.1159 
[9] 
SeungYeal Ha, Hansol Park. Emergent behaviors of the generalized Lohe matrix model. Discrete & Continuous Dynamical Systems  B, 2021, 26 (8) : 42274261. doi: 10.3934/dcdsb.2020286 
[10] 
Meiling Yang, Yongsheng Li, Zhijun Qiao. Persistence properties and wavebreaking criteria for a generalized twocomponent rotational bfamily system. Discrete & Continuous Dynamical Systems, 2020, 40 (4) : 24752493. doi: 10.3934/dcds.2020122 
[11] 
Jibin Li. Bifurcations and exact travelling wave solutions of the generalized twocomponent HunterSaxton system. Discrete & Continuous Dynamical Systems  B, 2014, 19 (6) : 17191729. doi: 10.3934/dcdsb.2014.19.1719 
[12] 
Shengfu Deng. Generalized multihump wave solutions of KdvKdv system of Boussinesq equations. Discrete & Continuous Dynamical Systems, 2019, 39 (7) : 36713716. doi: 10.3934/dcds.2019150 
[13] 
Caixia Chen, Shu Wen. Wave breaking phenomena and global solutions for a generalized periodic twocomponent CamassaHolm system. Discrete & Continuous Dynamical Systems, 2012, 32 (10) : 34593484. doi: 10.3934/dcds.2012.32.3459 
[14] 
Hisashi Okamoto, Takashi Sakajo, Marcus Wunsch. Steadystates and travelingwave solutions of the generalized ConstantinLaxMajda equation. Discrete & Continuous Dynamical Systems, 2014, 34 (8) : 31553170. doi: 10.3934/dcds.2014.34.3155 
[15] 
Rui Liu. Several new types of solitary wave solutions for the generalized CamassaHolmDegasperisProcesi equation. Communications on Pure & Applied Analysis, 2010, 9 (1) : 7790. doi: 10.3934/cpaa.2010.9.77 
[16] 
Jonathan E. Rubin. A nonlocal eigenvalue problem for the stability of a traveling wave in a neuronal medium. Discrete & Continuous Dynamical Systems, 2004, 10 (4) : 925940. doi: 10.3934/dcds.2004.10.925 
[17] 
SunHo Choi. Weighted energy method and long wave short wave decomposition on the linearized compressible NavierStokes equation. Networks & Heterogeneous Media, 2013, 8 (2) : 465479. doi: 10.3934/nhm.2013.8.465 
[18] 
Manh Hong Duong, Yulong Lu. An operator splitting scheme for the fractional kinetic FokkerPlanck equation. Discrete & Continuous Dynamical Systems, 2019, 39 (10) : 57075727. doi: 10.3934/dcds.2019250 
[19] 
Gen Nakamura, Michiyuki Watanabe. An inverse boundary value problem for a nonlinear wave equation. Inverse Problems & Imaging, 2008, 2 (1) : 121131. doi: 10.3934/ipi.2008.2.121 
[20] 
Xiaoli Feng, Meixia Zhao, Peijun Li, Xu Wang. An inverse source problem for the stochastic wave equation. Inverse Problems & Imaging, , () : . doi: 10.3934/ipi.2021055 
2020 Impact Factor: 1.639
Tools
Metrics
Other articles
by authors
[Back to Top]