The Dirichlet-Neumann boundary control problem associated with Maxwell’s equations in a cylindrical region. (English) Zbl 0594.49026

Russell, D. L.

SIAM J. Control Optimization 24, 199-229 (1986).

The paper deals with the controllability of the Maxwell equations \(curl \vec H=\epsilon (\partial \vec E/\partial t),\quad curl \vec E=-\mu (\partial H/\partial t),\quad div \vec E=\rho,\quad div \vec H=0\) with the initial conditions \(\vec E(x,y,z,0)=\vec H(x,y,z,0)=\vec 0\) and the boundary condition \(\mu \vec H_{\tau}(x,y,z,t)={\vec \nu}(x,y,z)\times \vec J(x,y,z,t)\) for (x,y,z)\(\in \Gamma\), where \(\vec H_{\tau}\) is the tangential component of \(\vec H\). By controllability is understood the possibility of transferring the initial field \(\vec E(x,y,z,0)\), \(\vec H(x,y,z,0)\) to a prescribed terminal field \(\vec E(x,y,z,T)\), \(\vec H(x,y,z,T)\) by means of a suitable boundary control current \(\vec J(x,y,z,t)\). The problem is considered on a cylindrical domain in \(R^ 3\). The cases of exact and approximate controllability are investigated.

Reviewer: I.Bock

MSC:

93B03	Attainable sets, reachability
35L15	Initial value problems for second-order hyperbolic equations
78A25	Electromagnetic theory (general)
35B37	PDE in connection with control problems (MSC2000)
35L20	Initial-boundary value problems for second-order hyperbolic equations
93B05	Controllability
93C20	Control/observation systems governed by partial differential equations
49J20	Existence theories for optimal control problems involving partial differential equations

Keywords:

controllability of the Maxwell equations; boundary control; exact and approximate controllability