To the solution of the Solonnikov-Fasano problem with boundary moving on arbitrary law x = γ(t). - Jenaliyev, M.T.; Ramazanov, M.I.; Tanin, A.O. (Bulletin of the Karaganda University. Mathematics Series, 2021)
In this paper we study the solvability of the boundary value problem for the heat equation in a domain that degenerates into a point at the initial moment of time. In this case, the boundary changing with time moves according to an arbitrary law x = γ(t). Using the generalized heat potentials, the problem under study is reduced to a pseudo-Volterra integral equation such that the norm of the integral operator is equal to one and it is shown that the corresponding homogeneous integral equation has a nonzero solution.