Time-Variant System Approximation via Later-Time Samples

Roza Aceska, Yeon Hyang Kim

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We develop a mathematical framework and efficient computational schemes to obtain an approximate solution of partial differential equations (PDEs) via sampled data. Recently, DeVore and Zuazua revisited the classical problem of inverse heat conduction, and they investigated how to recover the initial temperature distribution of a finite body from temperature measurements made at a fixed number of later times. In this paper, we consider a Laplace equation and a variable coefficient wave equation. We show that only one sensor employed at a crucial location at multiple time instances leads to a sequence of approximate solutions, which converges to the exact solution of these PDEs. This framework can be viewed as an extension of the novel, dynamical sampling techniques.

Original languageEnglish
Title of host publicationApproximation Theory XVI, 2019
EditorsGregory E. Fasshauer, Marian Neamtu, Larry L. Schumaker
PublisherSpringer
Pages1-9
Number of pages9
ISBN (Print)9783030574635
DOIs
StatePublished - 2021
EventInternational conference on Approximation Theory XVI, 2019 - Nashville, United States
Duration: May 19 2019May 22 2019

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume336
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational conference on Approximation Theory XVI, 2019
Country/TerritoryUnited States
CityNashville
Period05/19/1905/22/19

Keywords

  • Dynamical system
  • Evolutionary systems representations
  • Initial datum
  • Near-best approximation

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