Browse Journals

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

[3] T. K. Boni, On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order, Asympt. Anal. 21 (1999), 187-208.

[4] K. Bimpong-Bota, P. Ortoleva and J. Ross, Far- from equilibrium phenomenon at local sites of reactions, J. Chem. Phys. 60 (1974), 3124-3133.

[5] J. Bebernes and D. Eberly, Mathematical Problems from Combustion Theory, Applied Mathematical Sciences, 83, Springer, Berlin, 1989.

[6] C. Bandle and H. Brunner, Blow-up in diffusion equations: A survey, J. Comput. Appl. Math. 97 (1998), 3-22.

[7] C. Brändle, P. Groisman and J. D. Rossi, Fully discrete adaptive methods for a blow-up problem, Math. Model Meth. Appl. Sci. 14 (2004), 1425-1450.

[8] J. M. Chadam and H. M. Yin, A diffusion equation with localized chemical reactions, Proc. Edinb. Math. Soc. 37 (1994), 101-118.

[9] J. M. Chadam, A. Pierce and H. M. Yin, The blow-up property of solution to some differential equations with localized nonlinear reaction, J. Math. Anal. Appl. 169 (1992), 313-328.

[10] R. Ferreira, P. Groisman and J. D. Rossi, Adaptive numerical schemes for a parabolic problem with blow-up, IMA J. Numer. Anal. 23(3) (2003), 439-463.

[11] H. Fujita, On the blowing up of solutions to the Cauchy problem  J. Sci. Univ. Tokyo 13 (1966), 109-124.

[12] I. Fukuda and R. Suzuki, Quasilinear parabolic equations with localized reaction, (English summary), Adv. Differential Equations 10 (2005), 399-444.

[13] A. Friedman and A. A. Lacey, The blow-up time for solutions of nonlinear heat equations with small diffusion, SIAM J. Math. Anal. 18 (1987), 711-721.

[14] A. Friedman and B. McLeod, Blow-up of positive solutions of semi-linear heat equations, Indiana Univ. Math. J. 34 (1985), 425-477.

[15] P. Groisman and J. D. Rossi, Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions, J. Comput. Appl. Math. 135 (2001), 135-155.

[16] P. Groisman and J. D. Rossi, Dependence of the blow-up time with respect to parameters and numerical approximations for a parabolic problem, Asymptot. Anal. 37 (2004), 79-91.

[17] P. Groisman, Totally discrete explicit and semi-implicit Euler methods for a blow-up problem in several space dimensions, Computing 76 (2006), 325-352.

[18] T. K. Boni and Halima Nachid, Blow-up for semidiscretizations of some semilinear parabolic equations with nonlinear boundary conditions, Rev. Ivoir. Sci. Tech. 11 (2008), 61-70.

[19] T. K. Boni, Halima Nachid and Nabongo Diabate, Blow-up for discretization of a localized semilinear heat equation, Analele Stiintifice Ale Univertatii 2 (2010).

[20] Halima Nachid, Quenching for semi discretizations of a semilinear heat equation with potentiel and general non linearities, Revue D’analyse Numerique Et De Theorie De L’approximation 2 (2011), 164-181.

[21] Halima Nachid, Full discretizations of solution for a semilinear heat equation with Neumann boundary condition, Research and Communications in Mathematics and Mathematical Sciences 1 (2012), 53-85.

[22] Halima Nachid, Behavior of the numerical quenching time with a potential and general nonlinearities, Journal of Mathematical Sciences Advances and Application 15 (2012), 81-105.

[23] W. E. Olmstead and C. A. Roberts, Explosion in diffusive strip due to a concentrated nonlinear source, Methods Appl. Anal. 1 (1994), 434-445.

[24] H. A. Levine, The role of critical exponents in blow-up theorems, SIAM Rev. 32 (1990), 262-288.

[25] P. Ortoleva and J. Ross, Local structures in chemical reactions with heterogeneous catalysis, J. Chem. Phys. 56 (1972), 4397-4452.

[26] C. A. Roberts, Recent results on blow-up and quenching for nonlinear Volterra equations, J. Comput. Appl. Math. 205 (2007), 736-743.

[27] P. Souplet, Blow-up in nonlocal reaction-diffusion equation, SIAM. J. Math. Anal. 29 (1998), 1301-1334.

[28] P. Souplet, Uniform blow-up profiles and boundary behavior for diffusion equations with non-local nonlinear source, J. Differential Equations 153 (1999), 374-406.

[29] P. Souplet, Uniform blow-up profile and boundary behaviour for a non-local reaction-diffusion equation with critical damping, Math. Meth. Appl. Sci. 27 (2004), 1819-1829.

[30] L. Wang and Q. Chen, The asymptotic behavior of blow-up solution of localized nonlinear equation, J. Math. Anal. Appl. 200 (1996), 315-321.