2013/11/05 by Luisa Arlotti, Arlotti, Luisa, Bertrand Lods +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories #math.AP
paper · pdf · doi:10.48550/arxiv.1311.0971
arxiv created 2013/11/05 · openalex publication_date 2013/11/05 · arxiv updated 2013/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We revisit our study of general transport operator with general force field and general invariant measure by considering, in the L1 setting, the linear transport operator \TH associated to a linear and positive boundary operator H of unit norm. It is known that in this case an extension of \TH generates a substochastic (i.e. positive contraction) C0-semigroup (VH(t))t≥ 0. We show here that (VH(t))t≥ 0 is the smallest substochastic C0-semigroup with the above mentioned property and provides a representation of (VH(t))t ≥ 0 as the sum of an expansion series similar to Dyson-Phillips series. We develop an honesty theory for such boundary perturbations that allows to consider the honesty of trajectories on subintervals J ⊆ [0,∞). New necessary and sufficient conditions for a trajectory to be honest are given in terms of the aforementioned series expansion.