Parameter estimation for an infiltration problem

The Burgers equation is considered as a mathematical model for nonhysteretic infiltration in nonswelling soil under appropriate physical conditions. For this nonlinear partial differential equation, the modal approximation scheme for estimating parameters such as initial water distribution and precipitation-evaporation history is introduced. The function space parameter estimation convergence property of this scheme is proved. The idea is to change the nonlinear problem to a linear one by an appropriate change of variables. Also, numerical simulations are performed.