Recovery of an initial temperature from discrete sampling

Devore R, Zuazua E (2014)

Publication Type: Journal article

Publication year: 2014

Journal

Mathematical Models & Methods in Applied Sciences World Scientific Publishing

Book Volume: 24

Pages Range: 2487-2501

Journal Issue: 12

DOI: 10.1142/S0218202514500262

Abstract

The problem of recovering the initial temperature of a body from discrete temperature measurements made at later times is studied. While this problem has a general formulation, the results of this paper are only given in the simplest setting of a finite (one-dimensional), constant coefficient, linear rod. It is shown that with a judicious placement of a thermometer on this rod, the initial temperature profile of the rod can be completely determined by later time measurements. The paper then studies the number of measurements that are needed to recover the initial profile to a prescribed accuracy and provides an optimal reconstruction algorithm under the assumption that the initial profile is in a Sobolev class. © 2014 World Scientific Publishing Company.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Texas A&M University US United States (USA) (US) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

APA:

Devore, R., & Zuazua, E. (2014). Recovery of an initial temperature from discrete sampling. Mathematical Models & Methods in Applied Sciences, 24(12), 2487-2501. https://doi.org/10.1142/S0218202514500262

MLA:

Devore, Ronald, and Enrique Zuazua. "Recovery of an initial temperature from discrete sampling." Mathematical Models & Methods in Applied Sciences 24.12 (2014): 2487-2501.

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