Paper Info
Title
Maxwell's Equations as a Scattering Passive Linear System.
Abstract
We consider Maxwell's equations on a bounded domain O. R3 with Lipschitz boundary G, with boundary control and boundary observation. Relying on an abstract framework developed by us in an earlier paper, we define a scattering passive linear system that corresponds to Maxwell's equations and investigate its properties. The state of the system is BD , where B and D are the magnetic and electric flux densities, and the state space of the system is X = E. E, where E = L2(O; R3). We assume that G0 and G1 are disjoint, relatively open subsets of G such that G0. G1 = G. We consider G0 to be a superconductor, which means that on G0 the tangential component of the electric field is forced to be zero. The input and output space U consists of tangential vector fields of class L2 on G1. The input and output at any moment are suitable linear combinations of the tangential components of the electric and magnetic fields. The semigroup generator has the structure A = beta 0 -L L* G-.* R. P, where L = rot (with a suitable domain),. is the tangential component trace operator restricted to G1, R is a strictly positive pointwise multiplication operator on U (that can be chosen arbitrarily), and P-1 = mu 0 0 e is another strictly positive pointwise multiplication operator (acting on X). The operator -G is pointwise multiplication with the conductivity g = 0 of the material in O. The system is scattering conservative iff g = 0.
Year
DOI
Venue
2013
10.1137/120869444
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
Field
DocType
scattering passive system,scattering conservative system,Maxwell's equations,boundary control,boundary observation
Linear combination,Mathematical optimization,Linear system,Multiplication operator,Mathematical analysis,Tangential and normal components,Trace operator,Maxwell's equations,Mathematics,Pointwise,Bounded function
Journal
Volume
Issue
ISSN
51
5
0363-0129
Citations 
PageRank 
References 
4
0.61
4
Authors
2
Name
Order
Citations
PageRank
George Weiss131664.49
Olof J. Staffans26615.08