Reconstruction Of The Diffusion Parameter For The Bacterial Colony Model With Noised Measuring Point

This paper presents a procedure for estimating the diffusion parameter occurring in a bacterial colony model to ensure the best possible fit of the functions that describe the concentration of the nutrient and the density of the active bacteria to their known measurement values. The location of the measurement point and the measurements read from it are disturbed by errors of various values in order to demonstrate how these errors translate into the reconstructed results. The investigated solution procedure uses the following auxiliary methods: the finite element method combined with the method of lines to solve a corresponding direct problem and the Fibonacci search method to minimize an appropriately constructed functional.