Numerical quenching for a semilinear parabolic equation with a potential and general nonlinearities

• Boni, Théodore K. ^[1] ; Kouakou, Thibaut K. ^[2]
  1. [1] Institut National Polytechnique Houphout-Boigny.
  2. [2] Université d’Abobo-Adjamé.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 27, Nº. 3, 2008, págs. 259-287
• Idioma: inglés
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• Resumen

  • This paper concerns the study of the numerical approximation a semilinear parabolic equation subject to Neumann boundary conditions and positive initial data. We find some conditions under which the solution of a semidiscrete form of the above problem quenches in a fi- nite time and estimate its semidiscrete quenching time. We also prove that the semidiscrete quenching time converges to the real one when the mesh size goes to zero. A similar study has been also investigated taking a discrete form of the above problem. Finally, we give some numerical experiments to illustrate our analysis.