Determination of the Calcium channel distribution in the olfactory system
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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.
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
The authors would like to thanks the organizers of the congress “Partial Differential Equations, Optimal Design and Numerics”, held at Centro de Ciencias de Benasque Pedro Pascual, Benasque (Spain), and to the Basque Center for Applied Mathematics – BCAM, Bilbao (Spain), where part of this work was developed.
© 2014 by De Gruyter
Articles in the same Issue
- Frontmatter
- Acoustic impedance inversion with covariation approach
- An inverse problem for differential pencils on graphs with a cycle
- Analysis of the factorization method for a general class of boundary conditions
- Determination of the Calcium channel distribution in the olfactory system
- Locally extra-optimal regularizing algorithms
- The minimal radius of Galerkin information for severely ill-posed problems
Articles in the same Issue
- Frontmatter
- Acoustic impedance inversion with covariation approach
- An inverse problem for differential pencils on graphs with a cycle
- Analysis of the factorization method for a general class of boundary conditions
- Determination of the Calcium channel distribution in the olfactory system
- Locally extra-optimal regularizing algorithms
- The minimal radius of Galerkin information for severely ill-posed problems
