Inverse Problem for Fractional Diffusion Equation

Tuan, Vu Kim

Fractional Calculus and Applied Analysis (2011)

  • Volume: 14, Issue: 1, page 31-55
  • ISSN: 1311-0454

Abstract

top
MSC 2010: 26A33, 33E12, 34K29, 34L15, 35K57, 35R30We prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.

How to cite

top

Tuan, Vu Kim. "Inverse Problem for Fractional Diffusion Equation." Fractional Calculus and Applied Analysis 14.1 (2011): 31-55. <http://eudml.org/doc/219650>.

@article{Tuan2011,
abstract = {MSC 2010: 26A33, 33E12, 34K29, 34L15, 35K57, 35R30We prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.},
author = {Tuan, Vu Kim},
journal = {Fractional Calculus and Applied Analysis},
keywords = {Fractional Diffusion Equation; Inverse Problem; Boundary Spectral Data; Eigenfunction Expansion; fractional diffusion equation; inverse problem; boundary spectral data; eigenfunction expansion},
language = {eng},
number = {1},
pages = {31-55},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Inverse Problem for Fractional Diffusion Equation},
url = {http://eudml.org/doc/219650},
volume = {14},
year = {2011},
}

TY - JOUR
AU - Tuan, Vu Kim
TI - Inverse Problem for Fractional Diffusion Equation
JO - Fractional Calculus and Applied Analysis
PY - 2011
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 14
IS - 1
SP - 31
EP - 55
AB - MSC 2010: 26A33, 33E12, 34K29, 34L15, 35K57, 35R30We prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.
LA - eng
KW - Fractional Diffusion Equation; Inverse Problem; Boundary Spectral Data; Eigenfunction Expansion; fractional diffusion equation; inverse problem; boundary spectral data; eigenfunction expansion
UR - http://eudml.org/doc/219650
ER -

NotesEmbed ?

top

You must be logged in to post comments.