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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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Authors
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
- T. K. Boni, Extinction for discretizations of some semilinear parabolic equations, C.R.A.S, Serie I, 333 (2001), 795-800.
- T. K. Boni, H. Nachid and F. K. N'gohisse, Quenching time for a nonlocal diffusion problem with large initial data, Bull. Iran. Math. Soc., 35(2) (2009), 191-208.
- C. Y. Chan, New results in quenching. In Proceedings of the First World Congress of Nonlinear Analysts., Walter de Gruyter, New York, USA, (1996), 427-434.
- C. Y. Chan, Recent advances in quenching phenomena, Proc. Dynam. Sys. Appl., 2, 1996, 107-113.
- C. Y. Chan and Ozalp N. Beyond, quenching for singular reaction-diffusion mixed boundary-value problems., In Advances in Nonlinear Dynamics, Ed. S. Sivasundaram and A. A. Martynyuk, Gordon and Breach, Amsterdam, (2001), 217-227.
- C. W. Chang, Y. H. Hsu and H. T. Liu, Quenching behavior of parabolic problems with localized reaction term., IMathematics and Statistics, 2, (2014), 48-53.
- C. Y. Chan and S. I. Yuen, Parabolic problems with nonlinear absorptions and releases at the boundaries, Appl. Math. Comput, 121 (2001), 203-209.
- A. Friedman and A. A. Lacey, The blow-up time for solutions of nonlinear heat equations with small diusion, SIAM J. Math. Anal., 18 (1987), 711-721.
- S. C. Fu and J. S. Guo, Blow up for a semilinear reaction-diffusion system coupled in both equations and boundary conditions. J. Math. Anal. Appl., 276 (2002) 458-475.
- G. Gui and X. Wang, Life span of solutions of the Cauchy problem for a nonlinear heat equation, J. Di. Equat., 115 (1995), 162-172.
- H. Kawarada, On solutions of initial-boundary problem for ut = uxx+1=(1-u). Publ. Res. Inst. Math. Sci., 10 (1975), 729-736.
- C. M. Kirk and C. A. Roberts, A review of quenching results in the context of nonlinear volterra equations. Dynam. Cont. Dis. Ser. A, 10 (2003), 343-356.
- D. Nabongo and T. K. Boni, Quenching time of solutions for some nonlinear parabolic equations, An. St. Univ. Ovidus Constanta, 16(1) (2008), 91-106.
- A. De Pablo, F. Quiros and J. D. Rossi, Nonsimultaneous Quenching, Appl. Math. Letters, 15 (2002) 265-269.
- B. Selcuk and N. Ozalp, The quenching behavior of a semilinear heat equation with a singular boundary outflux. Q. Appl. Math., 72 (2014), 747-752.
- Numerical Approximation of the Quenching Time for One-Dimensional p-Laplacian with Singular Boundary Flux
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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
- L. M. Abia, J. C. L´o pez-Marcos and J. Mart´ınez, On the blow-up time convergence of semmidiscretizations of reaction-diffusion equations, Appl. Numer. Math., 26 (4) (1998), 399–414.
- L. M. Abia, J. C. L´opez-Marcos and J. Mart´ınez, On the blow-up for semmidiscretizations of reaction-diffusion equations, Appl. Numer. Math., 20 (1–2) (1996), 145–156.
- A. Anatoly, B. Murat and M. Mani, Crank-Nicolson type compact difference schemes for a loaded time-fractional hallaire equation, Fract. Calc. Appl. Anal., 24 (4) (2021), 1231–1256.
- E. Feireisl, H. Petzeltov´a and F. Simondon: Adminissible solutions for a class of non-linear parabolic problems with non-negative data, Proc. Roy. Soc. Edinburgh Sect., A 131 (2001), 857–883.
- M. Fila and H. A. Levine: Quenching on the boundary, Nonlinear Anal. TMA, 21 (1993), 795–802.
- H. Kawarada, On solutions of initial boundary problem ut = uxx + (1 − u)−1 , Plubl. Res. Inst. Math. Sci., 10 (1975), 729–736.
- F. Kong and Z. Luo, Solitary wave and periodic wave solutions for the non-Newtonian filtration equations with non-linear sources and a time varying delay, Acta Math. Sci., 37 (2017), 1803–1816.
- D. Nabongo and T. K. Boni, Quenching for semidiscretizations of heat equation with a singular boundary condition, Asymptot. Anal., 59 (1) (2008), 27–38.
- D. Nabongo and T. K. Boni, An adaptive schene to treat the phenomenon of quenching for a heat equation with non-linear boundar conditions, Numerical Analysis and Appl., 2 (2009), 87–98.
- K. N’Guessan and N. Diabat´e, Numerical quenching solutions of a parabolic equation Mogeling Electrostatic Mens, Gen. Math. Notes, 29 (1) (2015), 40–60.
- K. N’Guessan and N. Diabat´e, Blow up for discretization of some semilinear parabolic equation with a convection term, Global J. Pure Appl. Math., 12 (2016), 3367–3394.
- K. Nitin and M. Mani, Wavelet collocation method for fractional optimal control problems with fractional Bolza cost, Numer. Methods Partial Differential Equations, 37 (2) (2021), 1693–1724.
- K. Nitin and M. Mani, Method for solving non-linear fractional optimal control problems by using Hermite scaling function with error estimates, Optimal Control, Appl. Methods, 42 (2021), 417–444.
- Z. Wang, J. Yin and C. Wang, Critical exponents of the non-Newtonian polytropic filtration equation with nonlinear boundary conditions, Appl. Math. Letter, 20 (2007), 142–147.
- Y. Yang, J. Yin and C. Jin, A quenching phenomenon for one-dimensional p-Laplace with singular boundary flux, Appl. Math. Lett., 23 (2010), 955–959.