| [1] Astrita G, Marrucci G. Principles of Non-Newtonian Fluid Mechanics. New York: McGraw-Hill, 1974
[2] Cui Z J. Critical curves of the non-Newtonian polytropic filtration equations coupled with nonlinear boundary conditions. Nonlinear Anal, 2008, 68: 3201--3208
[3] Kalashnikov A S. Some problems of the qualitative theory of nonlinear degenerate parabolic equations of second order. Uspekhi Mat Nauk, 1987, 42: 135--176; English transl: Russian Math Surveys, 1987, 42: 169--222
[4] Zhou J, Mu C L. Critical curve for a non-Newtonian polytropic filtration system coupled via nonlinear boundary flux.
Nonlinear Anal, 2008, 68: 1--11
[5] Wang Z J, Yin J X, Wang C P. Critical exponents of the non-Newtonian polytropic filtration equation with nonlinear boundary condition. Appl Math Lett, 2007, 20: 142--147
[6] Wu Z Q, Zhao J N, Yin J X, Li H L. Nonlinear Diffusion Equations. River Edge, NJ: World Scientific Publishing Co Inc, 2001
[7] Vazquez J L. The Porous Medium Equations: Mathematical Theory. Oxford: Oxford University Press, 2007
[8] Dibenedetto E. Degenerate Parabolic Equations. Berlin, New York: Springer-Verlag, 1993
[9] Pao C V. Nonlinear Parabolic and Elliptic Equation. New York: Plenum, 1992
[10] Andreucci D, Tedeev A F. A Fujita type result for a degenerate Neumann problem in domains with noncompact boundary. J Math Anal Appl, 1999, 231: 543--567
[11] Fujita H. On the blowing up of solutions of the Cauchy problem for ut=Δu+u1+α. J Fac Sci Univ Tokyo Sect I, 1966, 13: 109--124
[12] Deng K, Levine H A. The role of critical exponents in blow-up theorems: the sequel. J Math Anal Appl, 2000, 243: 85--126
[13] Ferreira R, de Pablo A, Quiros F, Rossi J D. The blow-up profile for a fast diffusion equation with a nonlinear boundary condition. Rocky Mountain J Math, 2003, 33: 123--146
[14] Quiros F, Rossi J D. Blow-up set and Fujita-type curves for a degenerate parabolic system with nonlinear conditions.
Indiana Univ Math J, 2001, 50: 629--654
[15] Galaktionov V A, Levine H A. On critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary. Israel J Math, 1996, 94: 125--146
[16] Andreucci D, Tedeev A F. Optimal bounds and blow-up phenomena for parabolic problems in narrowing domains.
Proc Roy Soc Edinburgh Sect, 1998, 128A: 1163--1180
[17] Levine H A. The role of critical exponents in blow up theorems. SIAM Rev, 1990, 32: 262--288
[18] Galaktionov V A, Levine H A. A general approach to critical Fujita exponents and systems. Nonlinear Anal TMA, 1998, 34: 1005--1027
[19] Jin C H, Yin J X. Critical exponents and non-extinction for a fast diffusive polytropic filtration equation with nonlinear boundary sources. Nonlinear Anal, 2007, 67: 2217--2223
[20] Kalashnikov A S. On a nonlinear equation appearing in the theory of non-stationary filtration. Trudy Seminara I G Petrovski (in Russian), 1978
[21] Lieberman G M. Second Order Parabolic Differential Equations. River Edge: World Scientific, 1996
[22] Pablo A D, Quiros F, Rossi J D. Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition. IMA J Appl Math, 2002, 67: 69--98
[23] Song X, Zheng S. Blow-up and blow-up rate for a reaction-diffusion model with multiple nonlinearities. Nonlinear Anal, 2003, 54: 279--289
[24] Samarskii A A, Galaktionov V A, Kurdyumov S P, Mikhailov A P. Blow-up in Quasilinear Parabolic Equations. Berlin: Walter de Gruyter, 1995
[25] Wang S, Xie C H, Wang M X. Note on critical exponents for a system of heat equations coupled in the boundary conditions. J Math Anal Appl, 1998, 218: 313--324
[26] Xiang Z Y, Chen Q, Mu C L. Critical curves for degenerate parabolic equations coupled via non-linear boundary flux.
Appl Math Comput, 2007, 189: 549--559
[27] Zheng S N, Song X F, Jiang Z X. Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux. J Math Anal Appl, 2004, 298: 308--324
[28] Li Z P, Mu C L, Xie L. Critical curves for a degenerate parabolic equation with multiple nonlinearities. J Math Anal Appl, 2009, 359: 39--47 |