On one evolution equation of parabolic type with fractional differentiation operator in \(S\) spaces
type: Item
instance of: scholarly article
title: On one evolution equation of parabolic type with fractional differentiation operator in \(S\) spaces
zbMATH Open document ID: 1464.35408
DOI: 10.1155/2020/1673741
author: V. V. Gorodets'kyj
author: R. S. Kolisnyk
author: N. M. Shevchuk
published in: International Journal of Differential Equations
publication date: 2021-05-19T00:00:00Z
review text: Summary: In the paper, we investigate a nonlocal multipoint by a time problem for the evolution equation with the operator \(A= \left( I - \Delta\right)^{\omega / 2}\), \(\Delta=\left( \mathrm{d}^2 / \mathrm{d} x^2\right)\), and \(\omega\in [1; - 2)\) is a fixed parameter. The operator \(A\) is treated as a pseudodifferential operator in a certain space of type \(S\). The solvability of this problem is proved. The representation of the solution is given in the form of a convolution of the fundamental solution with the initial function which is an element of the space of generalized functions of ultradistribution type. The properties of the fundamental solution are investigated. The behavior of the solution at \(t\longrightarrow+\infty \) (solution stabilization) in the spaces of generalized functions of type \(S^\prime\) and the uniform stabilization of the solution to zero on \(\mathbb{R}\) are studied.
Mathematics Subject Classification ID: 35S10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K90
Mathematics Subject Classification ID: 46F05
zbMATH DE Number: 7349519
zbMATH Keywords: generalized functions of ultradistribution type
Wikidata QID: Q115243886
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/1673741
OpenAlex ID: W3043783658
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cites work: Two-point problem for a class of evolution equations. I
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description: scientific article; zbMATH DE number 7349519