Open AccessIdentifications for General Degenerate Problems of Hyperbolic Type in Hilbert Spaces
Author(s) -
Angelo Favini,
Gabriela Marinoschi,
Hiroki Tanabe,
Ya. Yakubov
Publication year - 2018
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2018-64-1-194-210
Subject(s) - hilbert space , degenerate energy levels , invertible matrix , mathematics , type (biology) , order (exchange) , pure mathematics , operator (biology) , space (punctuation) , combinatorics , mathematical physics , mathematical analysis , physics , quantum mechanics , chemistry , computer science , ecology , biochemistry , finance , repressor , gene , transcription factor , economics , biology , operating system
In a Hilbert space X, we consider the abstract problem M∗ddt(My(t))=Ly(t)+f(t)z,0≤t≤τ,My(0)=My0, where L is a closed linear operator in X and M∈L(X) is not necessarily invertible, z∈X. Given the additional information Φ[My(t)]=g(t) wuth Φ∈X∗, g∈C1([0,τ];C). We are concerned with the determination of the conditions under which we can identify f∈C([0,τ];C) such that y be a strict solution to the abstract problem, i.e., My∈C1([0,τ];X), Ly∈C([0,τ];X). A similar problem is considered for general second order equations in time. Various examples of these general problems are given.