Source: Rocky Mountain J. Math.
Volume 33, Number 1
D.G. Aronson, M.G. Crandall and L.A. Peletier, Stabilization of solutions of a degenerate nonlinear diffusion problem, Nonlinear Anal. 6 (1982), 1001-1022.
Mathematical Reviews (MathSciNet): MR678053
G.I. Barenblatt, On some unsteady motions of a liquid or a gas in a porous medium, Prikl. Mat. Mekh. 16 (1952), 67-78. (Russian)
Mathematical Reviews (MathSciNet): MR46217
--------, Scaling, self-similarity and intermediate asymptotics, Cambridge Univ. Press, Cambridge, UK, 1996.
E. Chasseigne and J.L. Vázquez, Theory of extended solutions for fast diffusion equations in optimal classes of data. Radiation from singularities, Arch. Rat. Mech. Anal. (2002), to appear.
M. Chlebík and M. Fila, On the blow-up rate for the heat equation with a nonlinear boundary condition, Math. Methods Appl. Sci. 23 (2000), 1323-1330.
--------, Some recent results on the blow-up on the boundary for the heat equation, Banach Center Publ., Vol. 52, Polish Academy of Science, Inst. of Math., Warsaw, 2000, pp. 61-71.
K. Deng and H. Levine, The role of critical exponents in blow-up theorems: The sequel, J. Math. Anal. Appl. 243 (2000), 85-126.
M. Fila and J. Filo, Blow-up on the boundary: A survey, in Singularities and differential equations (S. Janeczko et al., eds.), Banach Center Publ., Vol. 33, Polish Academy of Science, Inst. of Math., Warsaw, 1996, pp. 67-78.
M. Fila and P. Quittner, The blowup rate for the heat equation with a nonlinear boundary condition, Math. Methods Appl. Sci. 14 (1991), 197-205.
J. Filo, Diffusivity versus absorption through the boundary, J. Differential Equations 99 (1992), 281-305.
V.A. Galaktionov, On asymptotic self-similar behaviour for a quasilinear heat equation. Single point blow-up, SIAM J. Math. Anal. 26 (1995), 675-693.
V.A. Galaktionov and H.A. Levine, On critical Fujita exponents for heat equations with nonlinear flux boundary conditions on the boundary, Israel J. Math. 94 (1996), 125-146.
B.H. Gilding and L.A. Peletier, On a class of similarity solutions of the porous media equation, J. Math. Anal. Appl. 55 (1976), 351-364.
Mathematical Reviews (MathSciNet): MR436751
M.A. Herrero and M. Pierre, The Cauchy problem for $u_t=\D u^m$ when $0<m<1$, Trans. Amer. Math. Soc. 291 (1985), 145-158.
Mathematical Reviews (MathSciNet): MR797051
B. Hu, Remarks on the blowup estimate for solution of the heat equation with a nonlinear boundary condition, Differential Integral Equations 9 (1996), 891-901.
B. Hu and H.M. Yin, The profile near blow-up time for solutions of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc. 346 (1994), 117-135.
J. Hulshof, Similarity solutions of the porous medium equation with sign changes, J. Math. Anal. Appl. 157 (1991), 75-111.
C.W. Jones, On reducible nonlinear differential equations occurring in mechanics, Proc. Roy. Soc. London Ser. A 217 (1953), 327-343.
Mathematical Reviews (MathSciNet): MR54129
H.A. Levine, The role of critical exponents in blow up theorems, SIAM Rev. 32 (1990), 262-288.
--------, Some nonexistence and instability theorems for solutions of formally parabolic equations of the form $Pu_t=-Au+F(u)$, Arch. Rat. Mech. Anal. 51 (1973), 371-386.
Mathematical Reviews (MathSciNet): MR348216
G.M. Lieberman, Second order parabolic differential equations, World Scientific Publ., River Edge, NJ, 1996.
F.J. Mancebo and J.M. Vega, A model of porous catalyst accounting for incipiently non-isothermal effects, J. Differential Equations 151 (1999), 79-110.
A. de Pablo, F. Quirós and J.D. Rossi, Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition, IMA J. Appl. Math. 67 (2002), 69-98.
F. Quirós and J.D. Rossi, Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions, Indiana Univ. Math. J. 50 (2001), 629-654.
F. Quirós and J.L. Vázquez, Asymptotic behaviour of the porous media equation in an exterior domain, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), 183-227.
A.A. Samarskii, V.A. Galaktionov, S.P. Kurdyunov and A.P. Mikhailov, Blow-up in problems for quasilinear parabolic equations, Nauka, Moscow, 1987 (Russian). English transl., Walter de Gruyter, Berlin, 1995.
T.I. Zelenyak, Stabilization of solution of boundary value problems for a second order parabolic equation with one space variable, Differ. Uravn. 4 (1986), 34-45 (Russian). English transl., Differential Equations 4 (1986), 17-22.