### Abstract

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.

Language | English |
---|---|

Pages | 1081-1112 |

Number of pages | 32 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 72 |

Issue number | 4 |

Early online date | 15 Aug 2012 |

DOIs | |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- mathematical model
- capillary-fill device
- antibody-antigen
- Volterra equations
- existence and uniqueness
- asymptotic results
- regular perturbation
- numerical approximation

### Cite this

*SIAM Journal on Applied Mathematics*,

*72*(4), 1081-1112. https://doi.org/10.1137/110839965

}

*SIAM Journal on Applied Mathematics*, vol. 72, no. 4, pp. 1081-1112. https://doi.org/10.1137/110839965

**A mathematical treatment of the fluorescence capillary-fill device.** / Rebelo, Magda; Diogo, Teresa; McKee, Sean.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A mathematical treatment of the fluorescence capillary-fill device

AU - Rebelo, Magda

AU - Diogo, Teresa

AU - McKee, Sean

N1 - new copy of document added

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - mathematical model

KW - capillary-fill device

KW - antibody-antigen

KW - Volterra equations

KW - existence and uniqueness

KW - asymptotic results

KW - regular perturbation

KW - numerical approximation

UR - http://epubs.siam.org/siap/resource/1/smjmap

U2 - 10.1137/110839965

DO - 10.1137/110839965

M3 - Article

VL - 72

SP - 1081

EP - 1112

JO - SIAM Journal on Applied Mathematics

T2 - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 4

ER -