Advances in Differential Equations

An approximating family for the Dirichlet-to-Neumann semigroup

Hassan Emamirad and Idriss Laadnani

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper we prove that the Dirichlet-to-Neumann semigroup $S(t)$ is an analytic compact Markov irreducible semigroup in $C(\partial \Omega)$ in any bounded smooth domain $\Omega$. By a generalization of the Lax semigroup, we construct an approximating family for $S(t)$. We prove some regularizing characters and compactness of this family. By using the ergodic properties of $S(t)$, we deduce its asymptotic behavior. At the end we conjecture some open problems.

Article information

Source
Adv. Differential Equations Volume 11, Number 3 (2006), 241-257.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867709

Mathematical Reviews number (MathSciNet)
MR2221482

Zentralblatt MATH identifier
1112.47032

Subjects
Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
Secondary: 35P25: Scattering theory [See also 47A40] 47A40: Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]

Citation

Emamirad, Hassan; Laadnani, Idriss. An approximating family for the Dirichlet-to-Neumann semigroup. Adv. Differential Equations 11 (2006), no. 3, 241--257. https://projecteuclid.org/euclid.ade/1355867709.


Export citation