ArticleProceedings of the ... IEEE Conference on Decision & Control. IEEE Conference on Decision & Control2016
Control of reaction-diffusion equations on time-evolving manifolds.
Article in Proceedings of the ... IEEE Conference on Decision & Control. IEEE Conference on Decision & Control, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
2 citing papers in PubMed.
- Turing conditions for pattern forming systems on evolving manifolds.Journal of mathematical biology · 2021Article
- Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds.Bulletin of mathematical biology · 2019Article
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Authors and funding
4 authors.
Funding
Abstract
Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such signal. Meanwhile, the diffusion of the signal is itself affected by the changes in shape and size of the organism. In other words, there is a complete coupling between the diffusion of the signal and the change of the shapes. In this paper, we introduce a mathematical model to investigate such coupling. The shape is given by a manifold, that varies in time as the result of a deformation given by a transport equation. The signal is represented by a density, diffusing on the manifold via a diffusion equation. We show the non-commutativity of the transport and diffusion evolution by introducing a new concept of Lie bracket between the diffusion and the transport operator. We also provide numerical simulations showing this phenomenon.
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Registered trials
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