Approximate Solutions of Heat Conduction Problems in Multi-dimensional Cylinder Type Domain by Conservative Averaging Method - Part 1

摘要

In this paper the description of the simplest variant of conservative averaging method for partial differential (or integro-differential) equations in cylinder type domain is given. Different types of boundary conditions (both linear and non-linear) are considered. As application of the method the process of intensive steel quenching as the time inverse ill-posed problem for the hyperbolic heat conduction for is studied. The conservative averaging method leads to the inverse well-posed problem. This problem is solved in closed form.