EVOLUTIONARY PSEUDODIFFERENTIAL EQUATIONS WITH SMOOTH SYMBOLS IN S-TYPE SPACES

dc.contributor.author	Городецький, Василь Васильович
dc.contributor.author	Петришин, Роман Іванович
dc.contributor.author	Мартинюк, Ольга Василівна
dc.date.accessioned	2023-11-24T12:13:47Z
dc.date.available	2023-11-24T12:13:47Z
dc.date.issued	2023-11
dc.identifier.issn	1573-9376
dc.identifier.uri	https://archer.chnu.edu.ua/xmlui/handle/123456789/8155
dc.description.abstract	We study an evolutionary equation with an operator (i∂/∂x), where φ is a smooth function satisfying certain conditions. As special cases of this equation, we get a partial differential equation of parabolic type with derivatives of finite and infinite orders and an equation with certain operators of fractional differentiation. It is shown that the restriction of the operator (i∂/∂x) to some spaces of type S coincides with a pseudodifferential operator constructed according to the function φ regarded as a symbol. We establish the correct solvability of a nonlocal multipoint (in time) problem for an equation of this kind with an initial function, which is an element of the space of generalized functions of ultradistribution type. The properties of the fundamental solution of this problem are analyzed	uk_UA
dc.relation.ispartofseries	Ukrainian Mathematical Journal, Vol. 75, No. 6;
dc.title	EVOLUTIONARY PSEUDODIFFERENTIAL EQUATIONS WITH SMOOTH SYMBOLS IN S-TYPE SPACES	uk_UA
dc.type	Article	uk_UA