A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is `application/pdf`

.

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

2021
*
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS
*

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