Ir al contenido

Documat


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
  • DOI: 10.4067/S0716-09172008000300004
  • Enlaces
  • 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. 

  • Referencias bibliográficas
    • Citas [1] L. M. Abia, J. C. López-Marcos and J. Martinez, On the blowup time convergence of semidiscretizations of reaction-diffusion equations,...
    • [2] A. Acker and B. Kawohl, Remarks on quenching, Nonl. Anal. TMA, 13, pp. 53-61, (1989).
    • [3] T. K. Boni, Extinction for discretizations of some semilinear parabolic equations, C. R. Acad. Sci. Paris, S´ er. I, 333, pp. 795-800,...
    • [4] T. K. Boni, On quenching of solutions for some semilinear parabolic equations of second order, Bull. Belg. Math. Soc., 7, pp. 73-95, (2000).
    • [5] M. Fila, B. Kawohl and H. A. Levine, Quenching for quasilinear equations, Comm. Part. Diff. Equat., 17, pp. 593-614, (1992).
    • [6] J. S. Guo and B. Hu, The profile near quenching time for the solution of a singular semilinear heat equation, Proc. Edin. Math. Soc.,...
    • [7] J. Guo, On a quenching problem with Robin boundary condition, Nonl. Anal. TMA, 17, pp. 803-809, (1991).
    • [8] V. A. Galaktionov and J. L. Vázquez, Continuation of blowup solutions of nonlinear heat equations in several space dimensions, Comm. Pure...
    • [9] V. A. Galaktionov and J. L. Vázquez, The problem of blow-up in nonlinear parabolic equations, Discrete Contin. Systems A, 8, pp. 399-433,...
    • [10] M. A. Herrero and J. J. L. Velazquez, Generic behaviour of one dimensional blow up patterns, Ann. Scuola Norm. Sup. di Pisa, XIX, pp....
    • [11] C. M. Kirk and C. A. Roberts, A review of quenching results in the context of nonlinear volterra equations, Dyn. contin. Discrete Impuls....
    • [12] H. A. Levine, Quenching, nonquenching and beyond quenching for solutions of some parabolic equations, Annali Math. Pura Appl., 155),...
    • [13] K. W. Liang, P. Lin and R. C. E. Tan, Numerical solution of quenching problems using mesh-dependent variable temporal steps, Appl. Numer....
    • [14] K. W. Liang, P. Lin, M. T. Ong and R. C. E. Tan, A splitting moving mesh method for reaction-diffusion equations of quenching type, J....
    • [15] T. Nakagawa, Blowing up on the finite difference solution to ut= uxx+u2, Appl. Math. Optim., 2, pp. 337-350, (1976).
    • [16] D. Nabongo and T. K. Boni, Quenching for semidiscretization of a heat equation with a singular boundary condition, Asympt. Anal., 59,...
    • [17] D. Nabongo and T. K. Boni, Quenching time of solutions for some nonlinear parabolic equations, An. St. Univ. Ovidius Constanta, 16, pp....
    • [18] D. Nabongo and T. K. Boni, Quenching for semidiscretization of a semilinear heat equation with Dirichlet and Neumann boundary condition,...
    • [19] D. Nabongo and T. K. Boni, Numerical quenching for a semilinear parabolic equation, Math. Modelling and Anal., To appear.
    • [20] M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Prentice Hall, Englewood Cliffs, NJ, (1967).
    • [21] Q. Sheng and A. Q. M. Khaliq, Adaptive algorithms for convectiondiffusion-reaction equations of quenching type, Dyn. Contin. Discrete...
    • [22] Q. Sheng and A. Q. M. Khaliq, A compound adaptive approach to degenerate nonlinear quenching problems, Numer. Methods PDE, 15, pp. 29-47,...
    • [23] W. Walter, Differential-und Integral-Ungleichungen, Springer, Berlin, (1964).

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno