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arXiv · 1703.07616

Global existence, uniqueness and stability for nonlinear dissipative bulk-interface interaction systems

Karoline Disser
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Abstract

We show global well-posedness and exponential stability of equilibria for a general class of nonlinear dissipative bulk-interface systems. They correspond to thermodynamically consistent gradient structure models of bulk-interface interaction. The setting includes nonlinear slow and fast diffusion in the bulk and nonlinear coupled diffusion on the interface. Additional driving mechanisms can be included and non-smooth geometries and coefficients are admissible, to some extent. An important application are volume-surface reaction-diffusion systems with nonlinear coupled diffusion.

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Karoline Disser. 2020-01-03. Global existence, uniqueness and stability for nonlinear dissipative bulk-interface interaction systems. https://arxiv.org/abs/1703.07616

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