Advances in Differential Equations

An approximating family for the Dirichlet-to-Neumann semigroup

Hassan Emamirad and Idriss Laadnani

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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

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

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]


Emamirad, Hassan; Laadnani, Idriss. An approximating family for the Dirichlet-to-Neumann semigroup. Adv. Differential Equations 11 (2006), no. 3, 241--257.

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