American Institute of Mathematical Sciences

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May  2008, 7(3): 677-698. doi: 10.3934/cpaa.2008.7.677

Analysis of a biosensor model

Walter Allegretto 1, , Yanping Lin 2, and  Zhiyong Zhang 3,

1. 

Department of Mathematical Sciences, University of Alberta, Edmonton A B, Canada T6G 2G1
2. 

Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1
3. 

Department of Mathematics and Statistics, University of Alberta, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

Received  May 2007 Revised  September 2007 Published  February 2008

In this paper we consider a biosensor model in $R^3$, 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 $L^2$ spatial norm convergence properties. Finally, some illustrative numerical simulation results are presented.
Keywords: stability., finite volume method, Robin boundary condition, Biosensor model.
Mathematics Subject Classification: Primary: 35K55, 35D10; Secondary: 65M9.
Citation: Walter Allegretto, Yanping Lin, Zhiyong Zhang. Analysis of a biosensor model. Communications on Pure & Applied Analysis, 2008, 7 (3) : 677-698. doi: 10.3934/cpaa.2008.7.677
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