Stationary reaction–diffusion systems in L1

We prove existence of solutions to stationary [Formula: see text] reaction–diffusion systems where the data are in [Formula: see text] or in [Formula: see text]. We first give an abstract result where the “diffusions” are nonlinear [Formula: see text]-accretive operators in [Formula: see text] and the reactive terms are assumed to satisfy [Formula: see text] structural inequalities. It implies that the situation is controlled by an associated cross-diffusion system and provides [Formula: see text]-estimates on the reactive terms. Next we prove existence for specific systems modeling chemical reactions and which naturally satisfy less than [Formula: see text] structural (in)equalities. The main difficulty is also to obtain [Formula: see text]-estimates on the nonlinear reactive terms.