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Mathematical analysis of a PDE-ode coupled model of mitochondrial swelling with degenerate calcium ion diffusion.
SIAM J. Math. Anal. 52, 543-569 (2020)
The model that we investigate here is motivated by the mitochondria' swelling process controlled by calcium ions, the spatial dynamics of which is described by degenerate diffusion. We analyze the well-posedness and the long-term behavior of this PDE-ODE coupled system using a combination of variational methods with super- and subsolution arguments and properties of sublinear elliptic equations, and Lusin's theorem. We find that in order to be able to capture partial swelling in the long term the new model requires fewer structural assumptions on the nonlinear swelling rates than were required for a model with linear diffusion. Furthermore, if the nonlinear diffusion effects for calcium ions dominate over their production, in the long term all mitochondria will either be still intact or have completed swelling. On the other hand, if the calcium ion production dominates the nonlinear diffusion effects, some mitochodria will also remain in the intermediate state where swelling has been initiated but not completed.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Degenerate Diffusion ; Pde-ode Coupled System ; Long-time Behavior
ISSN (print) / ISBN 0036-1410
Quellenangaben Volume: 52, Issue: 1, Pages: 543-569
Publisher Society for Industrial and Applied Mathematics (SIAM)
Publishing Place 3600 Univ City Science Center, Philadelphia, Pa 19104-2688 Usa
Institute(s) Institute of Computational Biology (ICB)