@unpublished{WintergerstGugat, author = {Wintergerst, David and Gugat, Martin}, title = {Finite Time Blow-up of Traveling Wave Solutions for the Flow of Real Gas through Pipeline Networks}, pages = {12}, abstract = {In the context of gas transportation, analytical solutions are essential for the understanding of the underlying dynamics described by a system of partial differential equations. We derive traveling wave solutions for the 1-d isothermal Euler equations. A non-constant compressibility factor is used to describe the correlation between density and pressure. The blow-up of the traveling wave solution in � finite time is proven. We then extend our analysis to networks under appropriate coupling conditions and derive compatibility conditions to fulfill these coupling conditions.}, language = {en} }