# American Institute of Mathematical Sciences

## Stationary reaction-diffusion systems in $L^1$ revisited

 1 Université de Lorraine, B.P. 239, 54506 Vandœuvre-lès-Nancy, France 2 Ecole Normale Supérieure de Rennes and IRMAR, Campus de Ker Lann, 35170-Bruz, France

* Corresponding author: El Haj Laamri

Received  December 2019 Published  May 2020

We prove existence of $L^1$-weak solutions to the reaction-diffusion system obtained as a stationary version of the system arising for the evolution of concentrations in a reversible chemical reaction, coupled with space diffusion. This extends a previous result by the same authors where restrictive assumptions on the number of chemical species are removed.

Citation: El Haj Laamri, Michel Pierre. Stationary reaction-diffusion systems in $L^1$ revisited. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020355
##### References:
 [1] H. Brezis and W. A. Strauss, Semi-linear second-order elliptic equations in $L^1$, J. Math. Soc. Japan, 25 (4) (1973), 565-590. doi: 10.2969/jmsj/02540565.  Google Scholar [2] J. Fischer, Global existence of renormalized solutions to entropy-dissipating reaction-diffusion systems, Arch. Ration. Mech. Anal., 218 (1) (2015), 553-587. doi: 10.1007/s00205-015-0866-x.  Google Scholar [3] E. H. Laamri and M. Pierre, Stationary reaction-diffusion systems in $L^1$, M3AS, 28 (11) (2018), 2161-2190. doi: 10.1142/S0218202518400110.  Google Scholar [4] R. H. Martin and M. Pierre, Influence of mixed boundary conditions in some reaction-diffusion systems, Proc. Roy. Soc. Edinburgh, Sect. A, 127 (1997), 1053-1066. doi: 10.1017/S0308210500026883.  Google Scholar [5] M. Pierre, Global existence in reaction-diffusion systems with control of mass : a survey, Milan. J. Math., 78 (2010), 417-455. doi: 10.1007/s00032-010-0133-4.  Google Scholar

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##### References:
 [1] H. Brezis and W. A. Strauss, Semi-linear second-order elliptic equations in $L^1$, J. Math. Soc. Japan, 25 (4) (1973), 565-590. doi: 10.2969/jmsj/02540565.  Google Scholar [2] J. Fischer, Global existence of renormalized solutions to entropy-dissipating reaction-diffusion systems, Arch. Ration. Mech. Anal., 218 (1) (2015), 553-587. doi: 10.1007/s00205-015-0866-x.  Google Scholar [3] E. H. Laamri and M. Pierre, Stationary reaction-diffusion systems in $L^1$, M3AS, 28 (11) (2018), 2161-2190. doi: 10.1142/S0218202518400110.  Google Scholar [4] R. H. Martin and M. Pierre, Influence of mixed boundary conditions in some reaction-diffusion systems, Proc. Roy. Soc. Edinburgh, Sect. A, 127 (1997), 1053-1066. doi: 10.1017/S0308210500026883.  Google Scholar [5] M. Pierre, Global existence in reaction-diffusion systems with control of mass : a survey, Milan. J. Math., 78 (2010), 417-455. doi: 10.1007/s00032-010-0133-4.  Google Scholar
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