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Modeste, Camara Gninlfan
- Numerical Approximation of the Quenching Time for One-Dimensional p-Laplacian with Singular Boundary Flux
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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.