Abstract:
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 =
(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.
Key words: heat equation, moving boundary, degenerating domain, pseudo-Volterra integral equation.
