ON A SINGULAR HEAT EQUATION AND PARABOLIC BESSEL POTENTIAL

The main goal of this paper is to analyze the solution to the singular heat equation. A singular heat equation is the parabolic equation, where the Laplace-Bessel operator acts by spatial variables. We study its fundamental solution as well as the solution to the Cauchy problem. Also, we give semigroup properties for singular thermal potential, construct fractional powers of the Laplace-Bessel operator using Balakrishnan formulas, and consider parabolic Bessel potential. Finally, we prove the boundedness of the parabolic Bessel potential.