2020/10/05 by Martin Gugat, Gugat, Martin, Michaël Herty +1
Engineering · Mathematics · #35L65 #76N15 #82C40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Numerical Analysis (math.NA) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2010.02743
openalex publication_date 2020/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we survey recent progress on mathematical results on gas flow in pipe networks with a special focus on questions of control and stabilization. We briefly present the modeling of gas flow and coupling conditions for flow through vertices of a network. Our main focus is on gas models for spatially one-dimensional flow governed by hyperbolic balance laws. We survey results on classical solutions as well as weak solutions. We present results on well--posedness, controllability, feedback stabilization, the inclusion of uncertainty in the models and numerical methods.