Identification of the unknown diffusion coefficient in a linear parabolic equation via semigroup approach.
In: Advances in Difference Equations, Jg. 2014 (2014-12-01), Heft 1, S. 1-8
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Zugriff:
This article presents a semigroup approach to the mathematical analysis of the inverse parameter problems of identifying the unknown parameters p(t) and q in the linear parabolic equation ut(x,t) = uxx + qux(x,t) + p(t)u(x,t), with mixed boundary conditions ux(0,t) = Ψ0, k(1)u(1,t) = Ψ1. The main purpose of this paper is to investigate the distinguishability of the input-output mappingΦ[·] : P→H1,2[0,T], via semigroup theory. In this paper, it is shown that if the nullspace of the semigroup T(t) consists of only the zero function, then the input-output mappingΦ[·] has the distinguishability property. It is also shown that both types of boundary conditions and also the region in which the problem is defined play an important role in the distinguishability property of the input-output mapping. Moreover, the input data can be used to determine the unknown parameter p(t) at (x,t) = (0, 0) and also the unknown coefficient q. Furthermore, it is shown that measured output data f(t) can be determined analytically by an integral representation. Hence the input-output mappingΦ[·] : P→H1,2[0,T] is given explicitly in terms of the semigroup. [ABSTRACT FROM AUTHOR]
Titel: |
Identification of the unknown diffusion coefficient in a linear parabolic equation via semigroup approach.
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Autor/in / Beteiligte Person: | Ozbilge, Ebru ; Demir, Ali |
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Zeitschrift: | Advances in Difference Equations, Jg. 2014 (2014-12-01), Heft 1, S. 1-8 |
Veröffentlichung: | 2014 |
Medientyp: | academicJournal |
ISSN: | 1687-1839 (print) |
DOI: | 10.1186/1687-1847-2014-47 |
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