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This paper concerns the study of the numerical approximationfor the following initial-boundary value problem:utx; t = uxxx; t E1 - u0; t-p; x; t 2 -l; l x 0; T,u-l; t = 0; ul; t = 0; t in 0; T,ux; 0 = u0x andgt;= 0; x in -l; l,where p andgt; 1, l = 1-2 and E andgt; 0. Under some assumptions, we prove that the solution of a semidiscrete form of the above problem quenches in a nite time and estimate its semidiscrete quenching time. We also show that the semidiscrete quenching time in certain cases converges to the real one when the mesh size tends to zero. Finally,we give some numerical experiments to illustrate our analysis.

Tipo de documento: Artículo - Article

Palabras clave: Semidiscretizations, localized semilinear parabolic equation, semidiscrete quenching time, convergence.





Source: http://www.bdigital.unal.edu.co


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Boletı́n de Matemáticas Nueva Serie, Volumen XIV No.
2 (2007), pp.
92–109 NUMERICAL QUENCHING SOLUTIONS OF LOCALIZED SEMILINEAR PARABOLIC EQUATION DIABATE NABONGO (*) THÉODORE K.
BONI (**) Abstract.
This paper concerns the study of the numerical approximation for the following initial-boundary value problem:  −p    ut (x, t) = uxx (x, t) ε(1 − u(0, t)) , (x, t) ∈ (−l, l) × (0, T ), u(−l, t) = 0, u(l, t) = 0, t ∈ (0, T ),    u(x, 0) = u (x) ≥ 0, x ∈ (−l, l), 0 where p 1, l = 1 2 and ε 0.
Under some assumptions, we prove that the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its semidiscrete quenching time.
We also show that the semidiscrete quenching time in certain cases converges to the real one when the mesh size tends to zero.
Finally, we give some numerical experiments to illustrate our analysis. Key Words and Phrases.
Semidiscretizations, localized semilinear parabolic equation, semidiscrete quenching time, convergence. 2000 Mathematics Subject Classification: 35B40, 35B50, 35K60, 65M06. (*) Diabate Nabongo, Université d’Abobo-Adjamé, UFR-SFA, Département de Mathématiques et Informatiques, 16 BP 372 Abidjan 16, (Côte d’Ivoire), E-mail: nabongo diabate@yahoo.fr (**) Théodore K.
Boni, Institut National Polytechnique Houphouët-Boigny de Yamoussoukro, BP 1093 Yamoussoukro, (Côte d’Ivoire). 92 NUMERICAL QUENCHING SOLUTIONS OF LOCALIZED. 93 Resumen.
En este artı́culo se estudia la aproximación numérica para el siguiente problema de valor de frontera inicial:  −p    ut (x, t) = uxx (x, t) ε(1 − u(0, t)) , (x, t) ∈ (−l, l) × (0, T ), u(−l, t) = 0, u(l, t) = 0, t ∈ (0, T ),    u(x, 0) = u (x) ≥ 0, x ∈ (−l, l), 0 donde p 1, l = 1 2 y ε 0.
Bajo algunas hipótesis, probamos que la solución de una forma semidiscreta del problema anterior se satisface en un tiempo finito y esti...






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