Spectral problems for non elliptic symmetric systems with dissipative boundary conditions
Language
en
Article de revue
This item was published in
Journal of Functional Analysis. 2014-09-15, vol. 267, n° 6, p. 1637-1661
Elsevier
English Abstract
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 ...Read more >
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 $\partial_t - \sum_{j=1}^n A_j \partial_{x_j}$ in $\R^n,\: n \geq 3$, $n$ odd, in a smooth connected exterior domain $\Omega :=\R^n \setminus \bar{K}$. Assume that the rank of $A(\xi) = \sum_{j= 1}^n A_j \xi_j$ is constant for $\xi \not= 0.$ For maximally dissipative boundary conditions on $\Omega :=\R^n \setminus \bar{K}$ with bounded open domain $K$ the solution of the boundary problem in $\R^{+} \times \Omega$ is described by a contraction semigroup $V(t) = e^{t G_b},\:t \geq 0.$ Assuming coercive conditions for $G_b$ and its adjoint $G_b^*$ on the complement of their kernels, we prove that the spectrum of $G_b$ in the open half plane $\Re z < 0$ is formed only by isolated eigenvalues with finite multiplicities.Read less <
English Keywords
non elliptic symmetric system
dissipative boundary conditions
asymptotically disappearing solutions
Origin
Hal imported