Geodesic
Numerical quenching of a heat equation with nonlinear boundary conditions
Edja, Kouame Beranger 1 ; Toure, Kidjegbo Augustin 1 ; Koua, Brou Jean-Claude 2
1 Institut National Polytechnique Felix Houphouet-Boigny Yamoussoukro, BP 2444, Cote d'Ivoire
2 UFR Mathematique et Informatique, Universite Felix Houphouet Boigny, Cote d'Ivoire
Journal of nonlinear sciences and its applications, Tome 13 (2020) no. 1, p. 65-74.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we study the quenching behavior of semidiscretizations of the heat equation with nonlinear boundary conditions. We obtain some conditions under which the positive solution of the semidiscrete problem quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time and obtain some results on numerical quenching rate. Finally we give some numerical results to illustrate our analysis.
DOI : 10.22436/jnsa.013.01.06
Classification : 35K05, 34B15, 74S20
Keywords: Numerical quenching, heat equation, nonlinear boundary

Edja, Kouame Beranger  1 ; Toure, Kidjegbo Augustin  1 ; Koua, Brou Jean-Claude  2

1 Institut National Polytechnique Felix Houphouet-Boigny Yamoussoukro, BP 2444, Cote d'Ivoire
2 UFR Mathematique et Informatique, Universite Felix Houphouet Boigny, Cote d'Ivoire 
@article{JNSA_2020_13_1_a5,
     author = {Edja, Kouame Beranger  and Toure, Kidjegbo Augustin  and Koua, Brou Jean-Claude },
     title = {Numerical quenching of a heat equation with nonlinear  boundary conditions},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {65-74},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2020},
     doi = {10.22436/jnsa.013.01.06},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.013.01.06/}
}
TY  - JOUR
AU  - Edja, Kouame Beranger 
AU  - Toure, Kidjegbo Augustin 
AU  - Koua, Brou Jean-Claude 
TI  - Numerical quenching of a heat equation with nonlinear  boundary conditions
JO  - Journal of nonlinear sciences and its applications
PY  - 2020
SP  - 65
EP  - 74
VL  - 13
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.013.01.06/
DO  - 10.22436/jnsa.013.01.06
LA  - en
ID  - JNSA_2020_13_1_a5
ER  - 
%0 Journal Article
%A Edja, Kouame Beranger 
%A Toure, Kidjegbo Augustin 
%A Koua, Brou Jean-Claude 
%T Numerical quenching of a heat equation with nonlinear  boundary conditions
%J Journal of nonlinear sciences and its applications
%D 2020
%P 65-74
%V 13
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.013.01.06/
%R 10.22436/jnsa.013.01.06
%G en
%F JNSA_2020_13_1_a5
Edja, Kouame Beranger ; Toure, Kidjegbo Augustin ; Koua, Brou Jean-Claude . Numerical quenching of a heat equation with nonlinear  boundary conditions. Journal of nonlinear sciences and its applications, Tome 13 (2020) no. 1, p. 65-74. doi : 10.22436/jnsa.013.01.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.013.01.06/

[1] Adou, K. A.; Touré, K. A.; Coulibaly, A. Numerical study of the blow-up time of positive solutions of semilinear heat equations, Far East J. Appl. Math., Volume 4 (2018), pp. 291-308

[2] Boni, T. K. Extinction for discretizations of some semilinear parabolic equations, C. R. Acad. Sci. Paris Sér. I Math., Volume 333 (2001), pp. 795-800 | DOI | Zbl

[3] Boni, T. K.; Diby, B. Y. Quenching time of solutions for some nonlinear parabolic equations with Dirichlet boundary condition and a potential, Ann. Math. Inform., Volume 35 (2008), pp. 31-42 | Zbl

[4] Chan, C. Y.; Yuen, S. I. Parabolic problems with nonlinear absorptions and releases at the boundaries, Appl. Math. Comput., Volume 121 (2001), pp. 203-209 | Zbl | DOI

[5] Edja, K. B.; Touré, K. A.; Koua, B. J.-C. Numerical Blow-up for a Heat Equation with Nonlinear Boundary Conditions, J. Math. Res., Volume 10 (2018), pp. 119-128

[6] Kawarada, H. On Solutions of Initial-Boundary Problem for $u_t=u_{xx}+\frac{1}{1-u}$, Publ. RIMS, Kyoto Univ., Volume 10 (1975), pp. 729-736

[7] Krirk, C. M.; Roberts, C. A. A quenching problem for the heat equation, J. Integral Equations Appl., Volume 14 (2002), pp. 53-72 | Zbl

[8] Levine, H. A. The Quenching of Solutions of Linear Parabolic and Hyperbolic Equations with Nonlinear Boundary Conditions, SIAM J. Math. Anal., Volume 4 (1983), pp. 1139-1153 | Zbl | DOI

[9] Levine, H. A.; Montgomery, J. T. The quenching of solutions of some nonlinear parabolic equations, SIAM J. Math. Anal., Volume 11 (1980), pp. 842-847 | Zbl | DOI

[10] Liang, K. W.; Lin, P.; Tan, R. C. E. Numerical Solution of Quenching Problems Using Mesh-Dependent Variable Temporal Steps, Appl. Numer. Math., Volume 57 (2007), pp. 791-800 | DOI | Zbl

[11] Mathurin, T. M.; Augustin, T. K.; Patrice, M. E. Numerical approximation of the blow-up time for a semilinear parabolic equation with nonlinear boundary equation, Far East J. Math. Sci. (FJMS), Volume 60 (2012), pp. 125-167 | Zbl

[12] Nabongo, D.; Boni, T. K. Quenching for semidiscretizations of a heat equation with a singular boundary condition, Asymptot. Anal., Volume 59 (2008), pp. 27-38 | Zbl

[13] N'dri, K. C.; Touré, K. A.; Yoro, G. Numerical blow-up time for a parabolic equation with nonlinear boundary conditions, Int. J. Numer. Methods Appl., Volume 17 (2018), pp. 141-160

[14] Selçuk, B. Quenching behavior of a semilinear reaction-diffusion system with singular boundary condition, Turkish J. Math., Volume 40 (2016), pp. 166-180

[15] Selçuk, B.; Ozalp, N. The quenching behavior of a semilinear heat equation with a singular boundary outflux, Quart. Appl. Math., Volume 72 (2014), pp. 747-752 | Zbl

[16] Teixeira, M. G.; Rincon, M. A.; Liu, I.-S. Numerical analysis of quenching-Heat conduction in metallic materials, Appl. Math. Model., Volume 33 (2009), pp. 2464-2473 | Zbl | DOI

[17] Zhi, Y. H.; Mu, C. L. The quenching behavior of a nonlinear parabolic equation with nonlinear boundary outflux, Appl. Math. Comput., Volume 184 (2007), pp. 624-630 | Zbl | DOI

Cité par Sources :