Explicit transport semigroup associated to abstract boundary conditions

Luisa Arlotti

doi:10.3934/proc.2011.2011.102

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2011, Volume 2011: 102-111. Doi: 10.3934/proc.2011.2011.102 open access

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Explicit transport semigroup associated to abstract boundary conditions

Luisa Arlotti^1,

1.
Universitá degli Studi di Udine, 33100 Udine

Received: June 30, 2010

Revised: May 31, 2011

Published: August 2017

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Abstract

The linear transport operator associated with abstract bounded boundary conditions, $T_H$, is considered. It is shown that, in some particular cases, a convergent series similar to Dyson-Phillips series can be defined. Sufficient conditions assuring that the sum of this series is a C$_o$-semigroup generated by $T_H$ itself are given.

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Mathematics Subject Classification: Primary: 47D06, 47N50; Secondary: 82C40.

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