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

El Haj Laamri; Michel Pierre

doi:10.3934/dcdss.2020355

Article Contents

2021, Volume 14, Issue 2: 455-464. Doi: 10.3934/dcdss.2020355

This issue Previous Article A brief tribute to pierre baras Next Article A generalization of a criterion for the existence of solutions to semilinear elliptic equations

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

El Haj Laamri^1, , and
Michel Pierre^2,

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
^* Corresponding author: El Haj Laamri

Received: December 2019

Early access: May 2020

Published: February 2021

Abstract / Introduction Full Text(HTML) Related Papers Cited by

Abstract

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.

Keywords:

Mathematics Subject Classification: 35K10, 35K40, 35K57.

Citation:

Full Text(HTML)

Related Papers

Cited by

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.