Inverse problem for the heat equation and the Schrödinger equation on a tree

In this paper, we establish global Carleman estimates for the heat and Schrödinger equations on a network. The heat equation is considered on a general tree and the Schrödinger equation on a star-shaped tree. The Carleman inequalities are used to prove the Lipschitz stability for an inverse problem...

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Bibliographic Details
Published in:Inverse problems 2012-01, Vol.28 (1), p.015011-30
Main Authors: Ignat, Liviu I, Pazoto, Ademir F, Rosier, Lionel
Format: Article
Language:English
Subjects:
Analysis of PDEs
Boundaries
Carleman estimate
Estimates
Exact sciences and technology
heat equation
Heat equations
Inequalities
inverse problem
Inverse problems
Mathematical analysis
Mathematics
network
Physics
Schroedinger equation
Schrödinger equation
tree
Trees
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Summary:In this paper, we establish global Carleman estimates for the heat and Schrödinger equations on a network. The heat equation is considered on a general tree and the Schrödinger equation on a star-shaped tree. The Carleman inequalities are used to prove the Lipschitz stability for an inverse problem consisting in retrieving a stationary potential in the heat (resp. Schrödinger) equation from boundary measurements.
ISSN:0266-5611
1361-6420
DOI:10.1088/0266-5611/28/1/015011