Analysis of some biosensor models with surface effects

  • Author / Creator
    Zhang, Zhiyong
  • 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.

  • Subjects / Keywords
  • Graduation date
    Fall 2009
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.