TY - JOUR

T1 - Identifications for General Degenerate Problems of Hyperbolic Type in Hilbert Spaces

AU - Favini, A.

AU - Marinoschi, G.

AU - Tanabe, H.

AU - Yakubov, Ya

N1 - Publisher Copyright:
© 2022, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022/1

Y1 - 2022/1

N2 - In a Hilbert space X, we consider the abstract problemM∗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) with 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.

AB - In a Hilbert space X, we consider the abstract problemM∗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) with 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.

UR - http://www.scopus.com/inward/record.url?scp=85123473561&partnerID=8YFLogxK

U2 - 10.1007/s10958-022-05713-2

DO - 10.1007/s10958-022-05713-2

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AN - SCOPUS:85123473561

SN - 1072-3374

VL - 260

SP - 583

EP - 599

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

IS - 4

ER -