Nonlinear diffusion and viral spread through the leaf of a plant
| Autor: | María Jesús Munoz-Lopez, Peter M. Waterhouse, Maureen P. Edwards, Robert S. Anderssen |
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| Rok vydání: | 2016 |
| Předmět: |
0301 basic medicine
Applied Mathematics General Mathematics 0206 medical engineering Mathematical analysis Structure (category theory) General Physics and Astronomy 02 engineering and technology Symmetry (physics) 03 medical and health sciences 030104 developmental biology Reaction–diffusion system Nonlinear diffusion Viral spread 020602 bioinformatics Mathematics |
| Zdroj: | Zeitschrift für angewandte Mathematik und Physik. 67 |
| ISSN: | 1420-9039 0044-2275 |
| DOI: | 10.1007/s00033-016-0707-2 |
| Popis: | The spread of a virus through the leaf of a plant is both spatially and temporally causal in that the present status depends on the past and the spatial spread is compactly supported and progresses outwards. Such spatial spread is known to occur for certain nonlinear diffusion processes. The first compactly supported solution for nonlinear diffusion equations appears to be that of Pattle published in 1959. In that paper, no explanation is given as to how the solution was derived. Here, we show how the solution can be derived using Lie symmetry analysis. This lays a foundation for exploring the behavior of other choices for nonlinear diffusion and exploring the addition of reaction terms which do not eliminate the compactly supported structure. The implications associated with using the reaction–diffusion equation to model the spatial–temporal spread of a virus through the leaf of a plant are discussed. |
| Databáze: | OpenAIRE |
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