Abstract
We consider a question of global existence for two component volume-surface reaction-diffusion systems. The first of the components diffuses in a region, and then reacts on the boundary with the second component, which diffuses on the boundary. We show that if the first component is bounded a priori on any time interval, and the kinetic terms satisfy a generalized balancing condition, then both solutions exist globally. We also pose an open question in the opposite direction, and give some a priori estimates for associated m component systems.
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Morgan, J., Sharma, V. (2019). Martin’s Problem for Volume-Surface Reaction-Diffusion Systems. In: Chetverushkin, B., Fitzgibbon, W., Kuznetsov, Y., Neittaanmäki, P., Periaux, J., Pironneau, O. (eds) Contributions to Partial Differential Equations and Applications. Computational Methods in Applied Sciences, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-78325-3_19
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DOI: https://doi.org/10.1007/978-3-319-78325-3_19
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