On connection conditions through boundary layer of PNP system
We consider the dynamic PNP system, with assumptions of local electro-neutrality (LEN) and near global electro-neutrality (GLN), i.e., without $O(1)$ extra charge. There is boundary layer near domain boundary, which requires more computational efforts to resolve. A natural question is that, can we replace the boundary layer by some effective boundary/connection conditions and solve the bulk region directly? In this talk, we present some connection conditions for various boundary conditions of PNP system. Some examples will be discussed, including one combining PNP system with Hodgkin-Huxley (HH) model. Hopefully, this will provide some insights on deriving continuum equations on the macro-scale for cellular structures.