Recovering a scalar time dependent function in a multidimensional parabolic equation by a nonlocal boundary additional information
Articolo
Data di Pubblicazione:
2008
Citazione:
Recovering a scalar time dependent function in a multidimensional parabolic equation by a nonlocal boundary additional information / U. Fedus, A. Lorenzi. - In: JOURNAL OF INVERSE AND ILL-POSED PROBLEMS. - ISSN 0928-0219. - 16:4(2008), pp. 359-380.
Abstract:
In this paper we solve (locally in time and under suitable assumptions on the data) an identification problem related to a linear parabolic equation when the additional information is time-dependent and nonlocal in space. More exactly, our problem consists in recovering a (positive) time-dependent coefficient β in front of the time derivative. We prove a local in time existence, uniqueness and stability result when the data belong to suitable function spaces. Our basic tool is the Semigroup Theory of linear bounded operators.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Analytic semigroup theory; First-order differential equations in general Banach spaces; Locally in time existence and uniqueness results; Recovering an unknown time-dependent term from which the equation depends nonlinearly
Elenco autori:
U. Fedus, A. Lorenzi
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