Analysis of a biosensor model

Walter Allegretto, Yanping Lin, Zhiyong Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

In this paper we consider a biosensor model in R3, consisting of a coupled parabolic differential equation with Robin boundary condition and an ordinary differential equation. Theoretical analysis is done to show the existence and uniqueness of a Holder continuous solution based on a maximum principle, weak solution arguments. The long-time convergence to a steady state is also discussed as well as the system situation. Next, a finite volume method is applied to the model to obtain an approximate solution. Drawing in part on the analytical results given earlier, we establish the existence, stability and error estimates for the approximate solution, and derive L2 spatial norm convergence properties. Finally, some illustrative numerical simulation results are presented.
Original languageEnglish
Pages (from-to)677-698
Number of pages22
JournalCommunications on Pure and Applied Analysis
Volume7
Issue number3
Publication statusPublished - 1 May 2008
Externally publishedYes

Keywords

  • Biosensor model
  • Finite volume method
  • Robin boundary condition
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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