  The microscopic bidomain problem with FitzHhugh-Nagumo ionic transport is
studied in the $L_p\!-\!L_q$-framework. Reformulating the problem as a
semilinear evolution equation on the interface, local well-posedness is proved
in strong as well as in weak settings. We obtain solvability for initial data
in the critical spaces of the problem. For dimension $d\leq 3$, by means of
energy estimates and a recent result of Serrin type, global existence is shown.
Finally, stability of spatially constant equilibria is investigated, to the
result that the stability properties of such equilibria parallel those of the
classical FitzHugh-Nagumo system in ODE's. These properties of the bidomain
equations are obtained combining recent results on Dirichlet-to-Neumann
operators, on critical spaces for parabolic evolution equations, and
qualitative theory of evolution equations.
