A Study of an Inverse Boundary Value Problem for the Heat Conduction Equation

A mixed initial boundary value problem for the heat conduction equation is investigated and solved. The problem statement includes three intervals: the first one (0 → T1) describes heating of an internal combustion chamber and the second one (T1 → T2), the chamber cooling and slower cooling of its wall. The third interval describes natural cooling of the chamber wall when the chamber temperature coincides with that of the environment. The applicability of the Fourier transform in time to this problem is proved. This makes it possible to transform the governing equation to an ordinary differential equation. By using the resulting equation, an inverse boundary value problem for the heat conduction equation is solved by a nonlinear method of projection regularization, and an error estimate of the approximate solution is obtained.