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

Muvasharkhan Jenaliyev | Zendy; M.I. Ramazanov | Zendy; A.O. Tanin | Zendy

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To 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 -

bulletin of the karaganda university-mathematics

Language(s) - English

Resource type - Journals

eISSN - 2663-5011

pISSN - 2518-7929

DOI - 10.31489/2021m1/37-49

Subject(s) - mathematics , mathematical analysis , boundary value problem , heat equation , volterra integral equation , integral equation , norm (philosophy) , operator (biology) , domain (mathematical analysis) , homogeneous , boundary (topology) , moment (physics) , summation equation , 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.

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