  Several problems, issued from physics, biology or the medical science, lead
to parabolic equations set in two sub-domains separated by a membrane with
selective permeability to specific molecules. The corresponding boundary
conditions, describing the flow through the membrane, are compatible with mass
conservation and energy dissipation, and are called the Kedem-Katchalsky
conditions. Additionally, in these models, written as reaction-diffusion
systems, the reaction terms have a quadratic behaviour.
  M. Pierre and his collaborators have developed a complete $L^1$ theory for
reaction-diffusion systems with different diffusions. Here, we adapt this
theory to the membrane boundary conditions and prove the existence of weak
solutions when the initial data has only $L^1$ regularity using the truncation
method for the nonlinearities. In particular, we establish several estimates as
the $W^{1,1}$ regularity of the solutions. Also, a crucial step is to adapt the
fundamental $L^2$ (space, time) integrability lemma to our situation.
