Convergence analysis of a parabolic nonlinear system arising in biology. (English) Zbl 1276.65054
The paper investigates a system of semi-linear reaction-diffusion equations in a bounded domain as applicable to biological systems. The biological system presented in the paper consists of the decomposition of the organic matter by microorganism and is modeled through a reaction-diffusion equation with appropriate initial and boundary conditions. A finite element discretization is carried out and numerical results are presented for the evolution of the masses of the organic matter. Some theorems are also proved, however, the paper lacks analysis of the results.
Reviewer: K. N. Shukla (Gurgaon)
MSC:
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35K57 | Reaction-diffusion equations |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 35B09 | Positive solutions to PDEs |
| 92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
Keywords:
reaction-diffusion equation; finite element; convergence; error estimates; stability; evolution equations; parabolic system; positive solution; maximum principle; biological system; numerical resultsReferences:
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