On a class of problems of determining the temperature and density of heat sources given initial and final temperature

Abstract

We consider a class of problems modeling the process of determining the temperature and density of heat sources given initial and finite temperature. Their mathematical statements involve inverse problems for the heat equation in which, solving the equation, we have to find the unknown right-hand side depending only on the space variable. We prove the existence and uniqueness of classical solutions to the problem, solving the problem independently of whether the corresponding spectral problem (for the operator of multiple differentiation with not strongly regular boundary conditions) has a basis of generalized eigenfunctions. © 2012 Pleiades Publishing, Ltd.