On Lipschitz Solutions of Initial Boundary Value Problems for Balance Laws

Submission Status:accepted
  • The flow of gas through networks of pipes can be modeled by the isothermal Euler equations and algebraic node conditions that model the flow through the vertices of the network graph. We prove the well-posedness of the system for gas with nonconstant compressibility factor that is given by an affine linear function. We consider initial data and control functions that are Lipschitz continuous and compatible with the node and boundary conditions. We show the existence of semi--global Lipschitz continuous solutions of the initial boundary value problem. The construction of the solution is based upon a fixed point iteration along the characteristic curves. The solutions of the intial boundary value problem on arbitrary networks satisfy a maximum principle in terms of the Riemann invariants that states that the maximum of the absolute values is attained for the initial or the boundary data.

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  • On the existence, uniqueness and exact controllability of Lipschitz solutions of initial boundary value problems for gas networks with nonconstant compressibility factor

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Metadaten
Author:Martin Gugat, Stefan Ulbrich
Parent Title (English):Mathematical Models and Methods in Applied Sciences
Document Type:Article
Language:English
Date of Publication (online):2017/05/24
Date of first Publication:2017/07/03
Release Date:2017/07/03
Subprojects:A02
C03