Nonlinear perturbations of a class of holomorphic semigroups of growth order by comparison theorems for Volterra equations

Autor:	Naoki Tanaka, Toshitaka Matsumoto
Rok vydání:	2013
Předmět:	Semigroup Applied Mathematics Mathematical analysis Holomorphic functional calculus Holomorphic function Banach space Identity theorem Volterra integral equation Domain (mathematical analysis) symbols.namesake symbols Uniqueness Analysis Mathematics
Zdroj:	Nonlinear Analysis: Theory, Methods & Applications. 84:146-175
ISSN:	0362-546X
DOI:	10.1016/j.na.2013.02.016
Popis:	This paper studies nonlinear perturbation of a holomorphic semigroup of growth order α in a Banach space X . The generator A of a holomorphic semigroup is assumed to be almost sectorial and it is also assumed that the part A 0 in the closure X 0 of the domain D ( A ) is sectorial. A nonlinear perturbing operator B is assumed to be locally continuous from a subset of a real interpolation space between X 0 and D ( A 0 ) into X . Existence and uniqueness of mild solutions to the associated Cauchy problems are proved by using comparison theorems for integral equations of Volterra type. The result obtained is applied to show the global well-posedness of drift–diffusion systems with no-flux boundary conditions in the two dimensional case.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::0cfd9da1b4bc85ff8e78fdc16d4a688c https://doi.org/10.1016/j.na.2013.02.016 Zobrazit plný text záznamu Full Text from ScienceDirect