On improving an error estimate for a nonlinear projective regularization method when solving an inverse boundary value problem

The paper suggests a solution to a combined initial boundary value problem for the heat equation, in which, the heating takes place in the interval from $0$ to $T$, and then, starting with $T$, the free heat exchange with the surrounding medium occurs. Such a statement is an adequate mathematical model describing the temperature field of a heated object. The error estimation of the approximate solution to the problem is obtained in terms of the modulus of continuity of the inverse operator.