Uniqueness criterion in an inverse problem for an abstract differential equation with nonstationary inhomogeneous term

Autor:	Yu. S. Eidelman, I. V. Tikhonov
Rok vydání:	2005
Předmět:	Differential equation General Mathematics Operator (physics) Mathematical analysis Banach space Function (mathematics) Uniqueness Inverse problem C0-semigroup Eigenvalues and eigenvectors Mathematics
Zdroj:	Mathematical Notes. 77:246-262
ISSN:	1573-8876 0001-4346
DOI:	10.1007/s11006-005-0024-0
Popis:	In a Banach space E, we consider the inverse problem du(t)/dt = Au(t) + ϕ(t)p , u(0) = u0, u(T) = u1, with an unknown function u(t) and an element p ∈ E. The operator A is assumed linear and closed. In this paper, we establish minimal constraints on the function ϕ ∈ C([0, T]) for which the uniqueness of the solution of the inverse problem is completely described in terms of the eigenvalues of the operator A.
Databáze:	OpenAIRE
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