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The Phenomenon of Quenching for a Reaction-Diffusion System with Non-Linear Boundary Conditions


Affiliations
1 Department of Mathematics and Informatics, Universite Nangui Abrogoua, UFR-SFA, 02 BP 801 Abidjan, Côte d'Ivoire
2 Department of Mathematics and Informatics, Universite Peleforo Gon Coulibaly de Korhogo, UFR-Sciences Biologiques, BP 1328 Korhogo, Côte d'Ivoire
3 Department of Mathematics and Informatics, Universite Alassane Ouattara de Bouake, UFR-SED, 01 BP V 18 Bouake 01, Côte d'Ivoire
     

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We study the quenching behavior of the solution of a semi- linear reaction-diffusion system with nonlinear boundary conditions. We prove that the solution quenches in finite time and its quenching time goes to the one of the solution of the differential system. We also obtain lower and upper bounds for quenching time of the solution.

Keywords

Quenching, reaction-diffusion system, finite difference, numerical quenching time, nonlinear boundary condition, maximum principles
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  • The Phenomenon of Quenching for a Reaction-Diffusion System with Non-Linear Boundary Conditions

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Authors

Halima Nachid
Department of Mathematics and Informatics, Universite Nangui Abrogoua, UFR-SFA, 02 BP 801 Abidjan, Côte d'Ivoire
F. N'Gohisse
Department of Mathematics and Informatics, Universite Peleforo Gon Coulibaly de Korhogo, UFR-Sciences Biologiques, BP 1328 Korhogo, Côte d'Ivoire
N'Guessan Koffi
Department of Mathematics and Informatics, Universite Alassane Ouattara de Bouake, UFR-SED, 01 BP V 18 Bouake 01, Côte d'Ivoire

Abstract


We study the quenching behavior of the solution of a semi- linear reaction-diffusion system with nonlinear boundary conditions. We prove that the solution quenches in finite time and its quenching time goes to the one of the solution of the differential system. We also obtain lower and upper bounds for quenching time of the solution.

Keywords


Quenching, reaction-diffusion system, finite difference, numerical quenching time, nonlinear boundary condition, maximum principles

References





DOI: https://doi.org/10.18311/jims%2F2021%2F26056