Abstract
We consider two volume-surface reaction-diffusion systems arising from cell biology. The first system describes the localisation of the protein Lgl in the asymmetric division of Drosophila SOP stem cells, while the second system models the JAK2/STAT5 signalling pathway. Both model systems have in common that (i) different species are located in different spatial compartments, (ii) the involved chemical reaction kinetics between the species satisfies a complex balance condition and (iii) that the associated complex balance equilibrium is spatially inhomogeneous. By using recent advances on the entropy method for complex balanced reaction-diffusion systems, we show for both systems exponential convergence to the equilibrium with constants and rates, which can be explicitly estimated.
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Acknowledgements
The second author was supported by International Research Training Group IGDK 1754. This work has partially been supported by NAWI Graz.
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Fellner, K., Tang, B.Q. (2017). Entropy Methods and Convergence to Equilibrium for Volume-Surface Reaction-Diffusion Systems. In: Gonçalves, P., Soares, A. (eds) From Particle Systems to Partial Differential Equations. PSPDE 2015. Springer Proceedings in Mathematics & Statistics, vol 209. Springer, Cham. https://doi.org/10.1007/978-3-319-66839-0_8
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