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A brief tribute to pierre baras
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 |
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.
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. |
| [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. |
| [3] |
E. H. Laamri and M. Pierre, Stationary reaction-diffusion systems in $L^1$, M3AS, 28 (11) (2018), 2161-2190.
doi: 10.1142/S0218202518400110. |
| [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. |
| [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. |
show all references
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. |
| [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. |
| [3] |
E. H. Laamri and M. Pierre, Stationary reaction-diffusion systems in $L^1$, M3AS, 28 (11) (2018), 2161-2190.
doi: 10.1142/S0218202518400110. |
| [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. |
| [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. |
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