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Koffi, N'Guessan
- The Phenomenon of Quenching for a Reaction-Diffusion System with Non-Linear Boundary Conditions
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Affiliations
1 Department of Mathematics and Informatics, Universite Nangui Abrogoua, UFR-SFA, 02 BP 801 Abidjan, CI
2 Department of Mathematics and Informatics, Universite Peleforo Gon Coulibaly de Korhogo, UFR-Sciences Biologiques, BP 1328 Korhogo, CI
3 Department of Mathematics and Informatics, Universite Alassane Ouattara de Bouake, UFR-SED, 01 BP V 18 Bouake 01, CI
1 Department of Mathematics and Informatics, Universite Nangui Abrogoua, UFR-SFA, 02 BP 801 Abidjan, CI
2 Department of Mathematics and Informatics, Universite Peleforo Gon Coulibaly de Korhogo, UFR-Sciences Biologiques, BP 1328 Korhogo, CI
3 Department of Mathematics and Informatics, Universite Alassane Ouattara de Bouake, UFR-SED, 01 BP V 18 Bouake 01, CI
Source
The Journal of the Indian Mathematical Society, Vol 88, No 1-2 (2021), Pagination: 155–175Abstract
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
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Authors
Affiliations
1 Universit´e Alassane Ouattara de Bouak´e, UFR-SED, 01 BP V 18 Bouak´e 01, CI
2 Universit Flix Houphou¨et Boigny d’Abidjan, UFR-MI, 22 BP 582 Abidjan 22, CI
3 Universit´e F´elix Houphou¨et Boigny d’Abidjan, UFR-MI, 22 BP 582 Abidjan 22, CI
4 Institut National Polytechnique Houphou¨et-Boigny de Yamoussoukro, BP 2444 Yamoussoukro, CI
1 Universit´e Alassane Ouattara de Bouak´e, UFR-SED, 01 BP V 18 Bouak´e 01, CI
2 Universit Flix Houphou¨et Boigny d’Abidjan, UFR-MI, 22 BP 582 Abidjan 22, CI
3 Universit´e F´elix Houphou¨et Boigny d’Abidjan, UFR-MI, 22 BP 582 Abidjan 22, CI
4 Institut National Polytechnique Houphou¨et-Boigny de Yamoussoukro, BP 2444 Yamoussoukro, CI
Source
The Journal of the Indian Mathematical Society, Vol 90, No 1-2 (2023), Pagination: 85-104Abstract
This paper concerns the study of the numerical approximation for a discrete non-newtonian filtration system with nonlinear boundary conditions. We find some conditions under which the solution of a discrete form of above problem quenches in a finite time and estimate its discrete quenching time. We also establish the convergence of the discrete quenching time to the theoretical one when the mesh size tends to zero.Keywords
p-Laplacian, Discretization, Singular Boundary Flux, Discrete Quenching Time, Convergence.References
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