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

这个项目的目的是研究某些反问题 对于椭圆和抛物型偏微分方程， 未知系数是因变量的函数。 这些系数可以通过给出重叠的边界数据来恢复， 它规定狄利克雷 类型数据和选定的曲线位于 边界区域。该方法包括将逆 问题转化为一个不动点问题，其中一个有一个映射，从 未知系数的叠加数据。不动点问题是 通过迭代方案解决。作者能够 在某些情况下证明了该方案的收敛性。他们提出 现在有一些研究问题有待调查，以提高 技术的知识。 逆问题出现在许多应用中， 已经观察到的数据，问题是要找到参数的 描述这种现象的方程。连续介质力学， 数学 生物学和化学燃烧理论是潜在的应用之一 这种逆方法。

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.