Identifiability of operators for evolution equations in Banach spaces with an application to transport equations
type: Item
instance of: scholarly article
title: Identifiability of operators for evolution equations in Banach spaces with an application to transport equations
zbMATH Open document ID: 0808.34069
author: Shin-Ichi Nakagiri
author: M. Yamamoto
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-03-15T00:00:00Z
review text: In a Banach space \(X\) over the complex field \(C\), the equations \(du(t)/dt + A^ mu(t) = 0\) \((t \geq 0)\), \(u(0) = a^ m \in X\), \(dv(t)/dt + Av(t) = 0\) \((t \geq 0)\), \(v(0) = a \in X\), are considered. Here \(-A^ m\) and \(-A\) generate the \(C_ 0\)-semigroups \((\exp - tA^ m)_{t \geq 0}\) and \((\exp - tA)_{t \geq 0}\) respectively. The superscript \(m\) means quantities known as model systems. The problem of identifiability of operators and of initial values studied is the following: Let \(a^ m_ k\) \((1 \leq k \leq N)\) be known initial data and \(t_ 0 \geq 0\) be arbitrarily given. Under what conditions do the equalities \(\exp (- tA)a_ k = \exp (-tA^ m) a^ m_ k\) \((t \geq t_ 0\), \(1 \leq k \leq N)\) imply \(A = A^ m\) and \(a_ k = a^ m_ k\) \((1 \leq k \leq N)\)? Several abstract identifiability results are established by means of spectral theory for linear operators. As an application of these results, the identifiability of macroscopic total cross sections of transport equations is given.
reviewed by: Ion Onciulescu
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 34A55
zbMATH DE Number: 663713
zbMATH Keywords: Banach space
zbMATH Keywords: identifiability
zbMATH Keywords: spectral theory for linear operators
zbMATH Keywords: macroscopic total cross sections of transport equations
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1292
OpenAlex ID: W2042713473
DOI: 10.1006/JMAA.1994.1292
description: scientific article; zbMATH DE number 663713