SOLVABILITY OF BOUNDARY VALUE PROBLEMS FOR PARABOLIC AND ELLIPTIC EQUATIONS WITH THE BESSEL OPERATOR

The thesis studies boundary value problems for parabolic and elliptic equations containing the singular Bessel differential operator , . For the first boundary value problem for the singular heat equation and for the Dirichlet problem for the Weinstein equation in a rectangle, uniqueness is proved by the energy method and the extremum principle, and solutions are constructed as Fourier–Bessel series. Sufficient conditions on the data that guarantee convergence are given. The Cauchy problem on the half-axis is solved by the Hankel transform, which yields an explicit kernel expressed through the modified Bessel function. The results generalize the classical formulas for radially symmetric solutions of the heat and Laplace equations to an arbitrary “dimension” .