Rebelo, Magda and Diogo, Teresa and McKee, Sean (2012) *A mathematical treatment of the fluorescence capillary-fill device.* SIAM Journal on Applied Mathematics, 72 (4). pp. 1081-1112. ISSN 0036-1399

## Abstract

A mathematical model in the form of two coupled diffusion equations is provided for a competitive chemical reaction between an antigen and a labelled antigen for antibody sites on a cell wall; boundary conditions are such that the problem is both nonlinear and nonlocal. This is then re-characterized first as a pair of coupled singular integro-differential equations and then as a system of four Volterra integral equations. The latter permits a proof of existence and uniqueness of the solution of the original problem. Small and large time asymptotic solutions are derived and, from the first characterization, a regular perturbation solution is obtained. Numerical schemes are briefly discussed and graphical results are presented for human immunoglobulin.

Item type: | Article |
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ID code: | 39602 |

Notes: | new copy of document added |

Keywords: | mathematical model, capillary-fill device, antibody-antigen, Volterra equations, existence and uniqueness, asymptotic results, regular perturbation, numerical approximation, Probabilities. Mathematical statistics |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Pure Administrator |

Date Deposited: | 08 May 2012 16:02 |

Last modified: | 15 Mar 2013 16:50 |

URI: | http://strathprints.strath.ac.uk/id/eprint/39602 |

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