Solving of the Inverse Boundary Value Problem for the Heat Conduction Equation in Two Intervals of Time

The boundary value problem, BVP, for the PDE heat equation is studied and explained in this article. The problem declaration comprises two intervals; the (0, T) is the first interval and labels the heating of the inside burning chamber, and the second (T, infinity) interval defines the normal cooling of the chamber wall when the chamber temperature concurs with the ambient temperature. It is necessary to prove the boundary function of this problem has its place in the space H-1[0,infinity] in order to successfully apply the Fourier transform method. The applicability of the Fourier transform for time to this problem is verified. The method of projection regularization is used to solve the inverse boundary value problem for the heat equation and to obtain an evaluation for the error between the approximate and the real solution. These results are new and of practical interest as shown in the numerical case study.