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In this paper, we consider the source strength identification problem for the three-dimensional inverse heat conduction equations. The problem is to determine an unknown heat source strength from the measurement data for a specified location. In this process, the direct problem is solved by applying the Green's function method. Then, this problem can be converted into a Volterra integral equation of the first kind. Further, the Tikhonov and truncated singular value decomposition regularization methods are developed to identify the unknown source strength based on the discrepancy principle for choosing the regularization parameter. Finally, numerical examples are presented to show the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Release of pollution into rivers is required to be handled with special consideration to environmental standards. For this purpose, it is essential to specify the contribution of each pollution source in contamination of water resources. In this study, a mathematical model is proposed for determining locations and concentration release histories of polluting point sources using measured downstream river concentrations via an inverse problem framework. The inverse solution is based on the integral equation obtained from applying the Green's function method on the one-dimensional advection-dispersion contaminant transport equation. Discretization of this integral equation results in a linear, over-determined and ill-posed system of algebraic equations that are solved by using the Tikhonov regularization method. Several examples and some real field data are investigated to illustrate the abilities of the proposed model. Results imply that the proposed method is effective and can identify the pollution sources in rivers with acceptable accuracy. [ABSTRACT FROM AUTHOR]

In this article, I outline how integral equations and Green's functions are used in the courses that I teach, and how I believe my students benefit from exposure to these topics. [ABSTRACT FROM AUTHOR]