The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

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
     

   Subscribe/Renew Journal


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
Subscription Login to verify subscription
User
Notifications
Font Size



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

Abstract Views: 343  |  PDF Views: 0

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