On 2x2 Conservation Laws at a Junction

This paper deals with 2 × 2 conservation laws at a
junction. For the Cauchy problem, existence, uniqueness, and Lipschitz
continuous dependence of the solution from the initial data as well as
from the conditions at the junction are proved. The present
construction comprehends the case of the p-system used to describe gas
flow in networks and hereby unifies different approaches present in
the literature. Furthermore, different models for water networks are
considered.