Multi-dimensional electrochemistry model
The system (which is based on a standard model in electrochemistry) \[ {\partial u_i\over \partial t}= d_i\text{ div}(\nabla u_i+ \mu z_i u_i \nabla\varphi),\;i= 1,\dots, m,\;\mu> 0,\;d_i> 0,\;z_i\text{ is integer-valued}, \] \[ \varepsilon \Delta\varphi= - e\sum z_k u_k,\quad \varepsilon> 0,\quad e> 0 \] is considered together with given boundary and initial conditions. A priori time independent bounds for the solutions are obtained. The existence and uniqueness of steady- state solutions are proved. The main result concerns the global stability of the steady-state solutions.
scientific article; zbMATH DE number 797110
scientific article