In this paper we present the identification of parameters in the flux and diffusion functions for a quasilinear strongly degenerate parabolic equation which models the physical phenomenon of flocculated sedimentation. We formulate the identification problem as a minimization of a suitable cost function and we derive its formal gradient by means of adjoint equation which is a backward linear degenerate parabolic equation with discontinuous coefficients. For the numerical approach, we start with the discrete Lagrangian formulation and assuming that the direct problem is discretized by the Engquist-Osher scheme obtain a discrete adjoint state associated to this scheme. The conjugate gradient method permits to find numerically the physical parameters. In particular, it allows to identify as well the critical concentration level at which solid flocs begin to touch each other and determines the change of parabolic to hyperbolic behavior in the model equation.
