Well-posedness of space and time dependent transport equations on a network

2015/06/26 by Arne Roggensack, Roggensack, Arne
Computer Science · Engineering · Mathematics · #35L50 #35L65 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35R02 #Secondary 35F46 #Stability and Controllability of Differential Equations #math.AP #msc:35F46 #msc:35L50 #msc:35L65 #msc:35R02

paper · pdf · doi:10.48550/arxiv.1506.07966

arxiv created 2015/06/26 · openalex publication_date 2015/06/26 · arxiv updated 2015/06/29 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

This article is concerned with the study of weak solutions of a linear transport equation on a bounded domain with coupled boundary data for general non smooth space and time dependent velocity fields. The existence of solutions, its uniqueness and the continuous dependence of the solution on the initial and boundary data as well on the velocity is proven. The results are based on the renormalization property. At the end, the theory is shown to be applicable to the continuity equation on a network.

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