- We consider the identification of a nonlinear friction law in a one-dimensional
damped wave equation from additional boundary measurements. Well-posedness of the
governing semilinear hyperbolic system is established via semigroup theory and con-
traction arguments. We then investigte the inverse problem of recovering the unknown
nonlinear damping law from additional boundary measurements of the pressure drop
along the pipe. This coefficient inverse problem is shown to be ill-posed and a varia-
tional regularization method is considered for its stable solution. We prove existence of
minimizers for the Tikhonov functional and discuss the convergence of the regularized so-
lutions under an approximate source condition. The meaning of this condition and some
arguments for its validity are discussed in detail and numerical results are presented for
illustration of the theoretical findings