On a time nonlocal problem for inhomogeneous evolution equations

Autor:	Vladimir E. Fedorov, Natalia D. Ivanova, Yu. Yu. Fedorova
Rok vydání:	2014
Předmět:	Partial differential equation General Mathematics Weak solution Mathematical analysis Banach space Free boundary problem Boundary value problem C0-semigroup Linear equation Elliptic boundary value problem Mathematics
Zdroj:	Siberian Mathematical Journal. 55:721-733
ISSN:	1573-9260 0037-4466
Popis:	Under consideration is some problem for inhomogeneous differential evolution equation in Banach space with an operator that generates a C 0-continuous semigroup and a nonlocal integral condition in the sense of Stieltjes. In case the operator has continuous inhomogeneity in the graph norm. We give the necessary and sufficient conditions for existence of a generalized solution for the problem of whether the nonlocal data belong to the generator domain. Estimates on solution stability are given, and some conditions are obtained for existence of the classical solution of the nonlocal problem. All results are extended to a Sobolev-type linear equation, the equation in Banach space with a degenerate operator at the derivative. The time nonlocal problem for the partial differential equation, modeling a filtrating liquid free surface, illustrates the general statements.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a024dcdaa91e92c00fa2c2169dd9f512 https://doi.org/10.1134/s0037446614040144 Zobrazit plný text záznamu Plný text ve formátu PDF