Mathematical Sciences: Determination of Nonlinear Terms in Parabolic and Elliptic Partial Differential Equations and Overposed Data

点击翻译按钮获取中文摘要

The aim of this project is to investigate certain inverse problems for elliptic and parabolic partial differential equations that contain unknown coefficients which are functions of the dependent variables. These coefficients can be recovered by giving overposed boundary data, that it prescribed Dirichlet type data and a chosen curve lying on the boundary region. The method consists of converting the inverse problem into a fixed-point problem in which one has a mapping from the unknown coefficients to the overposed data. The fixed point problem is solved through an iteration scheme. The authors have been able to demonstrate the convergence of that scheme in some cases. They propose now a number of research questions to be investigated to improve the knowledge of the technique. The inverse problems arise in a number of applications where one has observed data and the problem is to find the parameters of the equation describing the phenomenon. Continuum mechanics, mathematical biology and chemical combustion theory are among potential applications of this inverse method.