Identification of Nonlinear Soil Physical Parameters from an Input-Output Experiment

Abstract

In the field of parameter identification in parabolic differential equations some theoretical and numerical results have been obtained in recent years. The linear heat equation with linear or nonlinear boundary conditions was studied by Cannon/Zachmann [1982]. Here the fact that the heat equation can be solved explicitely was used for various problems with overspecified boundary data to show existence and uniqueness of some unknown parameters. Nonlinear problems of the type ∂tu=∂x(D(u)∂xu) were treated by Cannon/DuChateau [1980], who showed that in some class of functions D( ) there exists at least one that fits overspecified boundary data best in a certain sense. DuChateau [1981] proved uniqueness of this function in a slightly different class.