Stationary reaction-diffusion systems in L 1

El Haj Laamri (1) , Michel Pierre (2, 3)

1 IECL - Institut Élie Cartan de Lorraine
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 ENS Rennes - École normale supérieure - Rennes

We prove existence of solutions to stationary m×m reaction-diffusion systems where the data are in L 1 or in LLogL. We first give an abstract result where the " diffusions " are nonlinear m-accretive operators in L 1 and the reactive terms are assumed to satisfy m structural inequalities. It implies that the situation is controlled by an associated cross-diffusion system and provides L 1-estimates on the reactive terms. Next we prove existence for specific systems modeling chemical reactions and which naturally satisfies less than m structural (in)equalities. The main difficulty is also to obtain L 1-estimates on the nonlinear reactive terms.

Mots clés: porous media; global existence; cross-diffusion; weak solutions; equation; reaction-diffusion systems; nonlinear diffusion

Domaines: Equations aux dérivées partielles [math.AP]

El Haj Laamri, Michel Pierre. Stationary reaction-diffusion systems in L 1. Mathematical Models and Methods in Applied Sciences, 2018, 28 (11), pp.2161-2190. ⟨10.1142/S0218202518400110⟩. ⟨hal-01748519⟩