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.
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.
| Original language | English |
|---|---|
| Pages (from-to) | 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 |
Keywords
- mathematical model
- capillary-fill device
- antibody-antigen
- Volterra equations
- existence and uniqueness
- asymptotic results
- regular perturbation
- numerical approximation