Stability and asymptotic analysis for instationary gas transport via relative energy estimates

Abstract We consider the transport of gas in long pipes and pipeline networks for which dynamics are dominated by friction at pipe walls. The governing equations can be formulated as an abstract dissipative Hamiltonian system allows us to derive perturbation bounds via relative energy estimates using a problem adapted nonlinear analysis. As particular consequences these results, we able prove stability with respect initial conditions model parameters conduct quantitative asymptotic analysis high limit. Our results established first flow single then extend our spirit energy-based port-Hamiltonian modelling.