Identifiability and stability of an inverse problem involving a Fredholm equation

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• 作者：Carlos Conca ; Rodrigo Lecaros ; Jaime H. Ortega…
• 关键词：Inverse problems ; Olfactory system ; Kernel determination ; Fredholm integral equation ; Partial differential equations ; Numerical reconstruction ; 35R20 ; 45B05 ; 45Q05 ; 65M32 ; 93B05
• 刊名：Chinese Annals of Mathematics - Series B
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：36
• 期：5
• 页码：737-762
• 全文大小：306 KB
• 参考文献：[1]Evans, L. C. and Gariepy, R. F., Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, Ann Arbor, London, 1992.
  [2]Flannery, R., French, D. A. and Kleene, S. J., Clustering of CNG channels in grass frog olfactory cilia, Biophysical J., 91, 2005, 179鈥?88.View Article
  [3]French, D. A. and Edwards, D. A., Perturbation approximation of solutions of a nonlinear inverse problem arising in olfaction experimentation, J. Math. Biol., 55, 2007, 745鈥?65.MathSciNet View Article
  [4]French, D. A., Flannery, R. J., Groetsch, C. W., et al., Numerical approximation of solutions of a nonlinear inverse problem arising in olfaction experimentation, Mathematical and Computer Modelling, 43, 2006, 945鈥?56.MathSciNet View Article
  [5]French, D. A. and Groetsch, C. W., Integral equation models for the inverse problem of biological ion channel distributions, Journal of Physics: Conference Series, 73(012006), 2007, 1742鈥?596.
  [6]Kleene, S. J., Origin of the chloride current in olfactory transduction, Neuron, 11, 1993, 123鈥?32.View Article
  [7]Kleene, S. J. and Gesteland, R. C., Calcium-activated chloride conductance in frog olfactory cilia, J. Neurosci., 11, 1991, 3624鈥?629.
  [8]Kleene, S. J. and Gesteland, R. C., Transmembrane currents in frog olfactory cilia, J. Membr. Biol., 120, 1991, 75鈥?1.View Article
  [9]Kleene, S. J., Gesteland, R. C. and Bryant, S. H., An electrophysiological survey of frog olfactory cilia, J. Exp. Biol., 195, 1994, 307鈥?28.
  [10]Titchmarsh, E. C., Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford, 1937.
  
• 作者单位：Carlos Conca (1)
  Rodrigo Lecaros (1)
  Jaime H. Ortega (1)
  Lionel Rosier (2)
  
  1. Centro de Modelamiento Matem谩tico and Departamento de Ingenier铆a Matem谩tica, Universidad de Chile (UMI CNRS 2807), Avda Beauchef 851, Edificio Norte, Casilla 170-3, Correo 3, Santiago, 8370459, Chile
  2. Centre Automatique et Syst猫mes, MINES ParisTech, PSL Research University, 60 Boulevard Saint-Michel, 75272, Paris, Cedex 06, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Applications of Mathematics
  Chinese Library of Science
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1860-6261

文摘

The authors study a linear inverse problem with a biological interpretation, which is modelled by a Fredholm integral equation of the first kind, where the kernel is represented by step functions. Based on different assumptions, identifiability, stability and reconstruction results are obtained.