Open AccessOperator cosine-functions and boundary value problems
Author(s) -
В. А. Костин,
A. V. Kostin,
D. V. Kostin
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524865531-536
Subject(s) - mathematics , boundary value problem , mathematical analysis , banach space , operator (biology) , cauchy distribution , poincaré–steklov operator , elliptic operator , initial value problem , dirichlet distribution , elliptic boundary value problem , differential operator , mixed boundary condition , robin boundary condition , biochemistry , chemistry , repressor , transcription factor , gene
For the first time, the theory of strongly continuous operator cosines of functions (COF) is applied to the study of the correct solvability of boundary value problems for second-order linear differential equations in Banach space (elliptic case). Usually in COF terms the correct solvability of the Cauchy problem (hyperbolic case) is formulated. The note specifies the conditions on the order of COF growth under which the Dirichlet boundary value problem is correct on the finite interval. The integral representation of the solution and its exact estimation are given.