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Global existence and uniqueness for a volume-surface reaction-nonlinear-diffusion system
Discrete and Continuous Dynamical Systems-Series S ( IF 1.8 ) Pub Date : 2020-04-13 , DOI: 10.3934/dcdss.2020326
Karoline Disser ,

We prove a global existence, uniqueness and regularity result for a two-species reaction-diffusion volume-surface system that includes nonlinear bulk diffusion and nonlinear (weak) cross diffusion on the active surface. A key feature is a proof of upper $ L^{\infty} $-bounds that exploits the entropic gradient structure of the system.

中文翻译:

体积-表面反应-非线性扩散系统的整体存在性和唯一性

我们证明了两种种群的反应扩散体积-表面系统的全局存在,唯一性和规则性结果,该系统包括在活性表面上的非线性体扩散和非线性(弱)交叉扩散。一个关键特征是上限$ L ^ {\ infty} $边界的证明,它利用了系统的熵梯度结构。
更新日期:2020-04-13
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