Vasyl Horodets'kyi, Ruslana Kolisnyk, Olha Martynyuk

A Nonlocal in Time Problem for a Singular Parabolic Equation

abstract:
In this paper, we study a nonlocal multipoint in time problem for the evolution equation with the pseudo-Bessel operator. We also prove the well-posedness of the above-mentioned problem with an initial function that is an element of a certain space of generalized functions, investigate the properties of the fundamental solution of the problem, and find a representation of the solution in the form of a convolution of the fundamental solution with the initial function.

Mathematics Subject Classification: 35K20, 35R10, 35S05, 35A08

Key words and phrases: Nonlocal problem, parabolic equations, fundamental solution, stabilization of the solution, well-posedness, spaces of generalized functions, pseudodifferential operator