Registro:

Referencias:

• Aronson, D.G., Crandall, M.G., Peletier, L.A., Stabilization of solutions of a degenerate nonlinear diffusion problem (1982) Nonlinear Anal, 16, pp. 1001-1022. , http://dx.doi.org/10.1016/0362-546X(82)90072-4
• Barenblatt, G.I., On some unsteady motions of a liquid or a gas in a porous medium (1952) Prikl. Mat. Meh., 16, pp. 67-78. , Russian
• (1996) Scaling, Self-similarity and Intermediate Asymptotics, , Cambridge University Press, Cambridge, U.K
• Chleb'ik, M., Fila, M., Some recent results on the blow-up on the boundary for the heat equation (2000) Banach Center Publ., 52, pp. 61-71
• Cortazár, C., Del Pino, M., Elgueta, M., On the blow-up set for ut = Δum + u m, m > 1 (1998) Indiana Univ. Math. J., 47, pp. 541-561. , http://dx.doi.org/10.1512/iumj.1998.47.1399
• Dal Passo, R., Luckaus, S., A degenerate diffusion problem not in divergence form (1987) J. Differential Equations, 69, pp. 1-14
• Deng, K., Levine, H., The role of critical exponents in blow-up theorems: The sequel (2000) J. Math. Anal. Appl., 243, pp. 85-126. , http://dx.doi.org/10.1006/jmaa.1999.6663
• Ferreira, R., De Pablo, A., Quirós, F., Rossi, J.D., The blow-up profile for a fast diffusion equation with a nonlinear boundary condition (2003) Rocky Mountain J. Math., 33, pp. 123-146
• Superfast quenching (2004) J. Differential Equations, 199, pp. 189-209. , http://dx.doi.org/10.1016/j-jde.2003.ll.001
• Fila, M., Filo, J., Blow-up on the boundary: A survey (1996) Banach Center Publ., 33, pp. 67-78. , Singularities and Differential Equations
• Fila, M., Quittner, P., The blowup rate for the heat equation with a nonlinear boundary condition (1991) Math. Methods Appl. Sci., 14, pp. 197-205. , http://dx.doi.org/10.1002/mma.1670140304
• Filo, J., Diffusivity versus absorption through the boundary (1992) J. Differential Equations, 99, pp. 281-305. , http://dx.doi.org/10.1016/0022-0396(92)90024-H, MR1184057 (94d:35083)
• Galaktionov, V.A., On asymptotic self-similar behaviour for a quasilinear heat equation. Single point blow-up (1995) SIAM J. Math. Anal., 26, pp. 675-693. , http://dx.doi.org/10.1137/S0036141093223419
• Galaktionov, V.A., Levine, H.A., On critical Fujita exponents for heat equations with nonlinear flux boundary conditions on the boundary (1996) Israel J. Math., 94, pp. 125-146
• Gilding, B.H., Herrero, M.A., Localization and blow-up of thermal waves in nonlinear beat conduction with peaking (1998) Math. Ann., 282, pp. 223-242
• Guo, J.S., Guo, Y.J., Tsai, J.Ch., Single-point blow-up patterns for a nonlinear parabolic equation (2003) Nonlinear Anal. TMA, 53, pp. 1149-1165. , http://dx.doi.org/10.1016/S0362-546X(03)00051-8
• Hu, B., Yin, H.M., The profile near blow-up time for solutions of the heat equation with a nonlinear boundary condition (1994) Trans. Amer. Math. Soc., 346, pp. 117-135
• Hulshof, J., Similarity solutions of the porous medium equation with sign changes (1991) J. Math. Anal. Appl., 157, pp. 75-111. , http://dx.doi.org/10.1016/0022-247X(91)90138-P
• Jones, C.W., On reducible non-linear differential equations occurring in mechanics (1953) Proc. Roy. Soc. London. Ser. A., 217, pp. 327-343. , MR0054129 (14,875a)
• Levine, H.A., The role of critical exponents in blow up theorems (1990) SIAM Rev., 32, pp. 262-288. , http://dx.doi.org/10.1137/1032046
• Mancebo, F.J., Vega, J.M., A model of porous catalyst accounting for incipiently non-isothermal effects (1999) J. Differential Equations, 151, pp. 79-110. , http://dx.doi.org/10.1006/jdeq.1999.3504
• Mlkhailov, A.P., Metastable localization of heat perturbations in a medium with nonlinear thermal conductivity (1977) Keldysh Inst. Appl. Math. Acad. Sci USSR, 64. , (preprint), (in Russian)
• De Pablo, A., Quiros, F., Rossi, J.D., Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition (2002) IMA J. Appl. Math., 67, pp. 69-98
• Samarskii, A.A., Galaktionov, V.A., Kurdyumov, S.P., Mikhailov, A.P., (1987) Blow-up in Problems for Quasilinear Parabolic Equations, , Nauka, Moscow, English transl.: Walter de Gruyter, Berlin, 1995. (Russian)
• Ughi, M., A degenerate parabolic equation modelling the spread of an epidemic (1986) Ann. Mat. Pura Appl, 143, pp. 385-400. , http://dx.doi.org/10.1007/BF01769226
• Zelenyak, T.I., Stabilization of solution of boundary value problems for a second-order parabolic equation with one space variable (1986) Differ. Uravn., 4, pp. 34-45
• (1986) Differential Eqns., 4, pp. 17-22. , English transi.: (Russian)

Citas:

---------- APA ----------

---------- CHICAGO ----------

---------- MLA ----------

---------- VANCOUVER ----------