Open AccessTo the solution of the Solonnikov-Fasano problem with boundary moving on arbitrary law x = γ(t).
Author(s) -
Muvasharkhan Jenaliyev,
M.I. Ramazanov,
A.O. Tanin
Publication year - 2021
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2021m1/37-49
Subject(s) - mathematics , boundary value problem , mathematical analysis , volterra integral equation , heat equation , integral equation , norm (philosophy) , domain (mathematical analysis) , operator (biology) , homogeneous , moment (physics) , boundary (topology) , law , physics , classical mechanics , combinatorics , biochemistry , chemistry , repressor , political science , transcription factor , gene
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.