In this paper, we prove the global exstence of weak solutions for a porous medium
dynamics of m species moving between two domains separated by a zero-thickness membrane.
On this membrane, Kedem–Katchalsky conditions are considered, and the study is characterized
by natural structural conditions applied to the nonlinear reactive terms. The global existence is
established under the assumption that these reactive terms are bounded in L1. This problem has
already been analyzed in the linear diffusion case by Ciavolella and Perthame in Ciavolella and
Perthame (2021, Journal of Evolution Equations 21, 1513–1540). The present work constitutes an
extensionfornonlineardiffusion,particularlyoftheporousmediumtype,intheform∂tvi−Δv
ri
=
i
Ri,foranexponentri <2.Thecaseri ≥2remainsanopenproblem.Thispaperisanadaptationof
the ideas from Ciavolella and Perthame (2021, Journal of Evolution Equations 21, 1513–1540), with
newstrategiestoovercometheappearanceofnonlinearityanddegeneracyinthediffusionterm.

Kedem–Katchalsky conditions, membrane boundary conditions, reaction–diffusion system,globalexistence,nonlineardiffusion.