Geodesic
On improving an error estimate for a nonlinear projective regularization method when solving an inverse boundary value problem
Eurasian journal of mathematical and computer applications, Tome 6 (2018) no. 3, pp. 53-74

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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.
Keywords: error estimation, modulus of continuity, Fourier transform, ill-posed problem. 
@article{EJMCA_2018_6_3_a3,
     author = {V. P. Tanana and A. I. Sidikova},
     title = {On improving an error estimate for a nonlinear projective regularization method when solving an inverse boundary value problem},
     journal = {Eurasian journal of mathematical and computer applications},
     pages = {53--74},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJMCA_2018_6_3_a3/}
}
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V. P. Tanana; A. I. Sidikova. On improving an error estimate for a nonlinear projective regularization method when solving an inverse boundary value problem. Eurasian journal of mathematical and computer applications, Tome 6 (2018) no. 3, pp. 53-74. http://geodesic.mathdoc.fr/item/EJMCA_2018_6_3_a3/