Explicit transport semigroup associated to abstract boundary conditions

Pages: 102 - 111, Issue Special, September 2011

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Luisa Arlotti - Universit√° degli Studi di Udine, 33100 Udine, Italy (email)

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.

Keywords:  Transport equations, Boundary conditions, Dyson-Phillips series
Mathematics Subject Classification:  Primary: 47D06, 47N50; Secondary: 82C40

Received: July 2010;      Revised: June 2011;      Published: October 2011.