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Analysis of some biosensor models with surface effects Open Access


Other title
biosensor model, surface effects
Type of item
Degree grantor
University of Alberta
Author or creator
Zhang, Zhiyong
Supervisor and department
Yanping Lin, Mathematical Science
Walter Allegretto, Mathematical Science
Examining committee member and department
Zihui Xia, Mechanical Engineering
Yau Shu Wong, Mathematical Science
Xinwei Yu, Mathematical Science
Xiaoqiang Zhao, Mathematical Science, Memorial University of Newfoundland
Department of Mathematical and Statistical Sciences

Date accepted
Graduation date
Doctor of Philosophy
Degree level
In this thesis, we study the mathematical modelling of some problems that involve surface effects. These include an optical biosensor, which uses optical principles qualitatively to convert chemical and biochemical concentrations into electrical signals. A typical sensor of this type was constructed in Badley et al., [6], and Jones et al., [18],but diffusion was considered in only one direction in [18] to simulate the reaction between the antigen and the antibody. For realistic applications, we propose the biosensor model in R3. Our theoretical approach is explicitly presented since it is simple and directly applicable to the numerical part of the thesis. In particular, we present existence and uniqueness results based on Maximum Principle and weak solution arguments. These ideas are later applied to systems and to the numerical analysis of the approximate discretized problems.It should be noted that without one dimensional symmetry, the equations can not be decoupled in order to reduce the problem to a single equation. We also show the long time monotonic convergence to the steady state. Next, a finite volume method is applied to the equations, and we obtain existence and uniqueness for the approximate solution as well as the convergence of the the first order temporal norm and the L2 spatial norm. We illustrate the results via some numerical simulations. Finally we consider a mathematically related system motivated by lagoon ecology. We show that under suitable conditions on the coe±cients, the system has a periodic solution under harvesting conditions. The mathematical techniques now depend on estimates for periodic parabolic problems.
License granted by Zhiyong Zhang ( on 2009-09-28T04:48:07Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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