Solução de problemas inversos do modelo Bevilacqua-Galeão de difusão anômala com dependência espacial

Abstract

The main objective of this dissertation is the formulation and solution of the direct and inverse problem for the anomalous diffusion bi-flux model proposed by Bevilacqua and Galeão. To solve both problems, a spatial variation for some model parameters was used. It was considered the free substances, that is, the fraction of available substance for the diffusion and also the parameter known as reactivity coefficient, with spatial variation. In relation to the direct problem, it was presented a monodimensional solution to the model using the Finite Difference Method, seeking to evidence the difference in the concentration profile of the solutions, comparing to the model results using variable and constant parameters. An inverse problem for parameters estimation, with spatial variation, was formulated and solved employing the Modified Luus-Jaakola (MLJ), Differential Evolution (DE) and Firefly (FF) stochastic methods. A sensitivity analyses was performed for each of the parameters, whose purpose was to identify optimal experimental conditions to enable the solution of the inverse problem. Through the results obtained in each case, it is possible to verify that the spatial variation of parameters directly affects the diffusion velocity. In relation to estimation of these parameters, the efficiency of each method used was observed, especially when the experimental data were noiseless. New formulations proposed by Bevilacqua were also discussed in this work.