Browse Journals

[1] L. M. Abia, J. C. López-Marcos and J. Martinez, On the blow-up time convergence of semidiscretizations of reaction-diffusion equations, Appl. Numer. Math. 26 (1998), 399-414.

[2] A. Acker and B. Kawohl, Remarks on quenching, Nonl. Anal. TMA 13 (1989), 53-61.

[3] T. K. Boni, Extinction for discretizations of some semilinear parabolic equations, C. R. A. S. Serie I 333 (2001), 795-800.

[4] T. K. Boni, On quenching of solutions for some semilinear parabolic equations of second order, Bull. Belg. Math. Soc. 7 (2000), 73-95.

[5] K. Deng and H. A. Levine, On the blow-up of  at quenching, Proc. Amer. Math. Soc. 106 (1989), 1049-1056.

[6] K. Deng and M. Xu, Quenching for a nonlinear diffusion equation with singular boundary condition, Z. Angew. Math. Phys. 50 (1999), 574-584.

[7] M. Fila and H. A. Levine, Quenching on the boundary, Nonl. Anal. TMA 21 (1993), 795-802.

[8] M. Fila, B. Kawohl and H. A. Levine, Quenching for quasilinear equations, Comm. Part. Diff. Equat. 17 (1992), 593-614.

[9] J. S. Guo and B. Hu, The profile near quenching time for the solution of a singular semilinear heat equation, Proc. Edin. Math. Soc. 40 (1997), 437-456.

[10] J. S. Guo, On a quenching problem with Robin boundary condition, Nonl. Anal. TMA 17 (1991), 803-809.

[11] V. A. Galaktionov and J. L. Vàzquez, Continuation of blow-up solutions of nonlinear heat equations in several space dimensions, Comm. Pure Appl. Math. 50 (1997), 1-67.

[12] V. A. Galaktionov and J. L. Vàzquez, The problem of blow-up in nonlinear parabolic equations, Discrete Contin. Systems A 8 (2002), 399-433.

[13] M. A. Herrero and J. J. L. Velazquez, Generic behaviour of one dimensional blow-up patterns, Ann. Scuola Norm. Sup. di Pisa XIX (1992), 381-950.

[14] C. M. Kirk and C. A. Roberts, A review of quenching results in the context of nonlinear Volterra equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A, Math. Anal. 10 (2003), 343-356.

[15] H. A. Levine, The Phenomenon of Quenching: A Survey, in Trends in the Theory and Practice of Nonlinear Analysis, North-Holland, Amsterdam, (1985), 275-286.

[16] H. A. Levine, Quenching, nonquenching and beyond quenching for solutions of some parabolic equations, Annali Math. Pura Appl. 155 (1990), 243-260.

[17] H. Kawarada, On solutions of initial-boundary problem for  Pul. Res. Inst. Math. Sci. 10 (1975), 729-736.

[18] K. W. Liang, P. Lin and R. C. E. Tan, Numerical solution of quenching problems using mesh-dependent variable temporal steps, Appl. Numer. Math. 57 (2007), 791-800.

[19] 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. Comput. Phys., to appear.

[20] T. Nakagawa, Blowing up on the finite difference solution to  Appl. Math. Optim. 2 (1976), 337-350.

[21] D. Phillips, Existence of solutions of quenching problems, Appl. Anal. 24 (1987), 253-264.

[22] M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice Hall, Englewood Cliffs, NJ, 1967.

[23] Q. Sheng and A. Q. M. Khaliq, Adaptive algorithms for convection-diffusion-reaction equations of quenching type, Dyn. Contin. Discrete Impuls. Syst. Ser. A, Math. Anal. 8 (2001), 129-148.

[24] Q. Sheng and A. Q. M. Khaliq, A compound adaptive approach to degenerate nonlinear quenching problems, Numer. Methods PDE 15 (1999), 29-47.

[25] W. Walter, Differential-und Integral-Ungleichungen, Springer, Berlin, 1964.