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

  • Biosensor model, surface effects

• Graduation date

  Fall 2009

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3269Z

• 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.