On recovering the solution of the Cauchy problem for the singular heat equation from incomplete inaccurate measurements

In 2009. G.G. Magaril-Ilyaev and K.Y. Osipenko set and solved the following problem. Let the temperature distributions in the form of functions of spatial variables, given approximated, be known at some points in time. For each set of such functions it is required to find a function that approximates the real temperature distribution at a given fixed moment of time in the best possible way. We study an analogous problem for a singular thermal type equation with a Bessel operator. Singularities of the specified type arise in models of mathematical physics in such cases when characteristics of media (for example, diffusion characteristics or heat conduction characteristics) have degenerate degree inhomogeneities. Besides, to such equations lead situations when isotropic diffusion processes with axial or spherical symmetry are investigated. Our results are in agreement with those of G.G. Magaril-Ilyaev and K.Y. Osipenko and reflect the peculiarities of the problem formulation.