Existence of local‐in‐time classical solutions of a model of flow in a bounded elastic tube

This paper studies the local‐in‐time existence of classical solutions to a hyperbolic system with differential boundary conditions modelling a flow in an elastic tube. The well‐known Lax transformations used for obtaining a priori estimates for conservation laws are difficult to apply here because of the inhomogeneity of the partial differential equations (PDE). Rather, our method relies on a suitable splitting of the original system into the PDE part and the ODE part, the characteristics for the PDE part, appropriate modulus of continuity estimates and a compactness argument. Copyright © 2016 John Wiley & Sons, Ltd.