To the solution of the Solonnikov-Fasano problem with boundary moving on arbitrary law x = γ(t)

M.T. Jenaliyev, Institute of Mathematics and Mathematical Modeling, M.I. Ramazanov, A.O. Tanin, Buketov Karaganda University, Buketov Karaganda University
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.
doi:10.31489/2021m1/37-49 fatcat:vl4kuomvwnfrxdmij3yjqdx43e