Series expansions of solutions of differential-difference parabolic equations

A. B. Muravnik^a, O. E. Yaremko^b, N. N. Yaremko<sup>c

a</sup> Peoples' Friendship University of Russia named after Patrice Lumumba, Moscow
^b Moscow State Technological University "Stankin"
^c National University of Science and Technology «MISIS», Moscow

Abstract: The Cauchy problem for parabolic differential-difference equations with operators that are sums of differential operators and translation operators and with operators that are their superpositions is investigated. Expansions of solutions of the indicated problem into function series are constructed. The domains of convergence (including uniform convergence) of the indicated series are established.

Keywords: differential-difference equation, parabolic equation, Cauchy problem, translation with respect to spatial variables, series expansion of solutions.

UDC: 517.956

PACS: 02.30.Jr

MSC: 47E07

Received: 18.12.2024

DOI: 10.4213/mzm14597

 English version: Mathematical Notes, 2025, 117:6, 1051–1064

Bibliographic databases:

•