Estimation of parameters in two-dimensional transport equations

摘要

A general approximation framework based on bicubic splines is developed for estimating temporally and spatially varying parameters in two-dimensional transport equations. The parameter estimation problem is first cast as an abstract infinite-dimensional minimization problem. Then a sequence of approximate, finite-dimensional minimization problems is defined, which yields a sequence of parameter estimates. Since convergence results relating the approximate problems to the full infinite-dimensional problem are presented in [6] and [17], this paper will focus only on the computer implementation of our technique and the results of numerical tests using analytically generated data. The technique is also applied to the analysis of actual biological data from an insect-dispersal experiment, in which the movement of cabbage-root flies in the presence of a cabbage crop was studied.