On One Evolution Equation of Parabolic Type with Fractional Differentiation Operator in S Spaces
Joint Authors
Gorodetskiy, V. V.
Kolisnyk, R. S.
Shevchuk, N. M.
Source
International Journal of Differential Equations
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-07-18
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
In the paper, we investigate a nonlocal multipoint by a time problem for the evolution equation with the operator A=I−Δω/2, Δ=d2/dx2, and ω∈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⟶+∞ (solution stabilization) in the spaces of generalized functions of type S′ and the uniform stabilization of the solution to zero on ℝ are studied.
American Psychological Association (APA)
Gorodetskiy, V. V.& Kolisnyk, R. S.& Shevchuk, N. M.. 2020. On One Evolution Equation of Parabolic Type with Fractional Differentiation Operator in S Spaces. International Journal of Differential Equations،Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1169906
Modern Language Association (MLA)
Gorodetskiy, V. V.…[et al.]. On One Evolution Equation of Parabolic Type with Fractional Differentiation Operator in S Spaces. International Journal of Differential Equations No. 2020 (2020), pp.1-11.
https://search.emarefa.net/detail/BIM-1169906
American Medical Association (AMA)
Gorodetskiy, V. V.& Kolisnyk, R. S.& Shevchuk, N. M.. On One Evolution Equation of Parabolic Type with Fractional Differentiation Operator in S Spaces. International Journal of Differential Equations. 2020. Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1169906
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1169906