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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Disser, Karoline¹ 

[1] Tech Univ Darmstadt, Fachbereich Math, AG Anal, Schlossgartenstr 7, D-64289 Darmstadt, Germany

关键词: Bulk-interface interaction;    Bulk-surface interaction;    Gradient structure;    Nonlinear diffusion;    Maximal parabolic regularity;   

DOI  :  10.1016/j.jde.2020.03.021

来源: Elsevier

【 摘 要 】

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. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free