Spectral problems for non-elliptic symmetric systems with dissipative boundary conditions

This paper considers and extends spectral and scattering theory to dissipative symmetric systems that may have zero speeds and in particular to strictly dissipative boundary conditions for Maxwell's equations. Consider symmetric systems partial derivative(t) - Sigma(n)(j=1) A(j)partial derivative(xJ) in R-n, n >= 3, n odd, in a smooth connected exterior domain Omega := R-n \ (K) over bar. Assume that the rank of A(xi) = Sigma(n)(j=1) A(j)xi(j) is constant for xi not equal 0. For maximally dissipative boundary conditions on Omega := R-n \ (K) over bar with bounded open domain K the solution of the boundary problem in R+ x Omega is described by a contraction semigroup V(t) = e(tGb) , t >= 0. Assuming coercive conditions for G(b) and its adjoint G(b)* on the complement of their kernels, we prove that the spectrum of Gb in the open half plane Re z < 0 is formed only by isolated eigenvalues with finite multiplicities. (C) 2014 Elsevier Inc. All rights reserved.