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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


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Online
ISSN
1569-3945
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Volume 22, Issue 5

Issues

Determination of the Calcium channel distribution in the olfactory system

Carlos Conca
  • Centro de Modelamiento Matemático (CMM) and Departamento de Ingeniería Matemática, Universidad de Chile (UMI CNRS 2807), Avenida Blanco Encalada 2120, Casilla 170-3, Correo 3, Santiago, Chile
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/ Rodrigo Lecaros
  • Centro de Modelamiento Matemático (CMM) and Departamento de Ingeniería Matemática, Universidad de Chile (UMI CNRS 2807), Avenida Blanco Encalada 2120, Casilla 170-3, Correo 3, Santiago, Chile; and Basque Center for Applied Mathematics – BCAM, Mazarredo 14, E-48009, Bilbao, Basque Country, Spain
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/ Jaime H. Ortega
  • Centro de Modelamiento Matemático (CMM) and Departamento de Ingeniería Matemática, Universidad de Chile (UMI CNRS 2807), Avenida Blanco Encalada 2120, Casilla 170-3, Correo 3, Santiago, Chile
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/ Lionel Rosier
Published Online: 2014-02-25 | DOI: https://doi.org/10.1515/jip-2013-0033

Abstract

In this paper we study a linear inverse problem with a biological interpretation, which is modeled by a Fredholm integral equation of the first kind. When the kernel in the Fredholm equation is represented by step functions, we obtain identifiability, stability and reconstruction results. Furthermore, we provide a numerical reconstruction algorithm for the kernel, whose main feature is that a non-regular mesh has to be used to ensure the invertibility of the matrix representing the numerical discretization of the system. Finally, a second identifiability result for a polynomial approximation of degree less than nine of the kernel is also established.

Keywords: Inverse problems; olfactory system; kernel determination; partial differential equations; numerical reconstruction

MSC: 35R20; 65M32; 92B05; 35K05

About the article

Received: 2013-05-15

Published Online: 2014-02-25

Published in Print: 2014-10-01


Funding Source: Basal-CMM project

Funding Source: Basal

Award identifier / Grant number: CeBeyBi

Funding Source: ECOS-CONICYT

Award identifier / Grant number: C13E05

Funding Source: FONDECYT

Award identifier / Grant number: 1140773

Funding Source: FONDECYT

Award identifier / Grant number: 111102

Funding Source: “Agence Nationale de la Recherche”, Project CISIFS

Award identifier / Grant number: ANR-09-BLAN-0213-02


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 22, Issue 5, Pages 671–711, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2013-0033.

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