Completeness of products of solutions and some inverse problems for PDE
type: Item
instance of: scholarly article
title: Completeness of products of solutions and some inverse problems for PDE
zbMATH Open document ID: 0728.35141
DOI: 10.1016/0022-0396(91)90051-A
published in: Journal of Differential Equations
publication date: 1991-01-01T00:00:00Z
review text: Building on the completeness of products of solutions to general differential equations, the author solves inverse problems for such equations. For example, if \(\Omega \subset {\mathbb{R}}^ 2\) is a bounded domain, and \(u_ 1,u_ 2\in H^ 2(\Omega \times (0,T))\) are solutions of an initial-boundary value problem for the equation \(\partial^ 2u_ j/\partial t^ 2-\Delta u_ j+a_ ju_ j=0\) on \(\Omega\times (0,T)\), then the coincidence of \(u_ 1\) and \(u_ 2\), and \(\partial u_ 1/\partial t\) and \(\partial u_ 2/\partial t\), on the boundary implies that \(a_ 1=a_ 2\).
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35L10
zbMATH DE Number: 4202945
zbMATH Keywords: uniqueness
zbMATH Keywords: general differential equations
zbMATH Keywords: inverse problems
author: Victor Isakov
reviewed by: Jürgen Appell
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4202945