A new approach to transport equations associated to a regular field: trace results and well-posedness

2006/10/26 by Luisa Arlotti, Arlotti, Luisa, Jacek Banasiak +3
Computer Science · Mathematics · Physics and Astronomy · #35F05 #47D05 #47D06 #47N55 #82C40 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #math-ph #math.AP #math.MP #msc:35F05 #msc:47D05 #msc:47D06 #msc:47N55 #msc:82C40

paper · pdf · doi:10.48550/arxiv.math/0610808

30 pages

openalex publication_date 2006/10/26 · arxiv created 2009/01/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize known results on transport equations associated to a Lipschitz field F on some subspace of ℝ^N endowed with some general space measure μ. We provide a new definition of both the transport operator and the trace measures over the incoming and outgoing parts of ∂ Ω generalizing known results from the literature. We also prove the well-posedness of some suitable boundary-value transport problems and describe in full generality the generator of the transport semigroup with no-incoming boundary conditions.

Related

• An L^p--approach to the well-posedness of transport equations associated to a regular field
• An Overview on Some Results Concerning the Transport Equation and its Applications to Conservation Laws
• Well-posedness of space and time dependent transport equations on a network
• Existence and uniqueness for the transport of currents by Lipschitz vector fields
• The trace problem for vector fields satisfying Hörmander's condition