On the construction of a potential from Cauchy data
type: Item
instance of: scholarly article
title: On the construction of a potential from Cauchy data
zbMATH Open document ID: 0788.65116
DOI: 10.1016/0377-0427(93)90060-O
author: Lester F. jun. Caudill
author: Bruce D. Lowe
published in: Journal of Computational and Applied Mathematics
publication date: 1994-05-30T00:00:00Z
review text: The authors consider the problem of determining the potential \(q(y)\in l^ \alpha(0,1)\) in the differential equation \(-\Delta u+ g(y)u= 0\), \((x,y)\in (0,1)\times (0,1)\); \(u(0,y)= u(1,y)= u(x,0)=0\), \(u(x,1)= f(x)\), \(u_ y(x,1)= g(x)\), where the condition \(f(0)= f(1)= 0\) is satisfied. The method of separation of variables is used to reduce the uniqueness question to the nonstandard inverse Sturm-Liouville problem. An asymptotic formula is developed that suggests that under appropriate conditions on the Cauchy pair \((f,g)\), \(q(y)\) is uniquely determined up to the mean. The authors give a numerical scheme for the recovery of \(q\). Numerical examples and the asymptotics show that reconstructing \(q\) from such data is similar to finding a function from its moments.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 490551
zbMATH Keywords: inverse problem
zbMATH Keywords: numerical examples
zbMATH Keywords: potential
zbMATH Keywords: separation of variables
zbMATH Keywords: inverse Sturm-Liouville problem
reviewed by: Karel Najzar
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 490551