Recovering variable order differential operators on star-type graphs from spectra

Yurko, V. A.

doi:10.1134/s0012266113120033

Cited by 10 publications

(13 citation statements)

References 13 publications

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“…In this paper we study the general case of variable order differential equations on star-type graphs. The obtained results are natural generalizations of the well-known results on inverse problems for differential operators on an interval and on graphs and, in particular, generalizations of the results from [24]- [25]. Moreover, we consider general matching conditions in the interior vertex.…”

Section: Introductionsupporting

confidence: 56%

“…This inverse problem is a generalization of the well-known inverse problems for differential operators on an interval and on graphs ( [23], [25]). In Section 5 we provide a constructive procedure for the solution of Inverse Problem 1 and prove its uniqueness.…”

Section: Formulation Of the Inverse Problemmentioning

confidence: 99%

“…In [24]- [25] the inverse spectral problem is considered for a very particular case of variable order differential equations on star-type graphs when there are only two differential equations with different orders. In this paper we study the general case of variable order differential equations on star-type graphs.…”

Section: Introductionmentioning

confidence: 99%

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Inverse Problem for Differential Operators on Spatial Networks with Different Orders on Different Edges

Yurko

2014

Trans. Moscow Math. Soc.

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We study the inverse problem of recovering differential operators from spectra on compact star-type graphs when differential equations have different orders on different edges. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.2010 Mathematics Subject Classification. Primary 34A55, 34L05, 47E05. License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use Licensed to Univ of Pittsburgh. Prepared on Sun Aug 2 10:59:40 EDT 2015 for download from IP 132.174.255.116. License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use INVERSE PROBLEM FOR DIFFERENTIAL OPERATORS 105and matching conditions for variable order differential operators on graphs [24]. Denote by Λ skμ = {λ lskμ } the eigenvalues of L skμ (counting with multiplicities). The inverse problem is formulated as follows. Fix N = 1, m.

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Section: Introductionsupporting

confidence: 56%

Section: Formulation Of the Inverse Problemmentioning

confidence: 99%

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Inverse Problem for Differential Operators on Spatial Networks with Different Orders on Different Edges

Yurko

2014

Trans. Moscow Math. Soc.

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“…The function Ψ sk is called the Weyl solution of order k with respect to the boundary vertex This inverse problem was solved in [48], where the uniqueness theorem was proved and an algorithm for the solution of Inverse problem 4.9 was obtained.…”

Section: Inverse Problems For Variable Order Operators On Graphs Withmentioning

confidence: 99%

“…Such problems are studied only recently, and nowadays they are investigated insufficiently. In [48][49][50] inverse spectral problems are considered for variable order operators on compact graphs (see also subsections 4.2 and 4.3 of the present paper). In this subsection, in contrast to the works [48][49][50], we study the inverse spectral problem on a noncompact graph.…”

Section: Variable Order Operators On a Noncompact With A Cyclementioning

confidence: 99%

Uniqueness of Recovering Arbitrary Order Differential Operators on Noncompact Spatial Networks

Yurko¹

2012

MMI

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We give a short review of results on inverse spectral problems for ordinary differential operators on a spatial networks (geometrical graphs). We pay the main attention to the most important nonlinear inverse problems of recovering coefficients of differential equations from spectral characteristics provided that the structure of the graph is known a priori. In the first half of the review we provide results related to inverse Sturm-Liouville problems on arbitrary compact graphs. Further, results on inverse problems for arbitrary order differential operators on compact graphs are presented. At the end we provide the main results on inverse problems on noncompact graphs.Bibliography: 55 titles.

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Inverse problems for differential operators of variable orders on star-type graphs: general case

Yurko

2014

Anal.Math.Phys.

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Recovering variable order differential operators on star-type graphs from spectra

Cited by 10 publications

References 13 publications

Inverse Problem for Differential Operators on Spatial Networks with Different Orders on Different Edges

Inverse Problem for Differential Operators on Spatial Networks with Different Orders on Different Edges

Uniqueness of Recovering Arbitrary Order Differential Operators on Noncompact Spatial Networks

Inverse problems for differential operators of variable orders on star-type graphs: general case

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