[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]Deng K, Levine H A. The role of critical exponents in blow-up theorems: The sequel J Math Anal Appl, 2000, 243: 85--126
[4]Dibenedetto E. Degenerate Parabolic Equations. Berlin, New York: Springer-Verlag, 1993
[5]Ferreira R, 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
[6]Fujita H. On the blowing up of solutions of the Cauchy problem for ut=Δu+u1+α. J Fac Sci Univ, 1966, 13: 109--124
[7]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
[8]Galaktionov V A, Levine H A. A general approach to critical Fujita exponents and systems. Nonlinear Anal, 1998, 34: 1005--1027
[9]Ivanov A V. Hoder estimates for quasilinear doubly degenerate parabolic equations. J Soviet Math, 1991, 56: 2320--2347
[10]Jiang Z X, Zheng S N. Doubly degenerate paralolic equation with nonlinear inner sources or boundary flux. Doctor Thesis. Dalian University of Tcchnology, In China, 2009
[11]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
[12]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
[13]Levine H A. The role of critical exponents in blow up theorems. SIAM Rev, 1990, 32: 262--288
[14] Li Z P, Mu C L. Critical curves for fast diffusive polytropic filtration equation coupled via nonlinear boundary flux. J Math Anal Appl, 2008, 346: 55--64
[15]Li Z P, Mu C L. Critical curves for fast diffusive on-Newtonian equation coupled via nonlinear boundary flux. J Math Anal Appl, 2008, 340: 876--883
[16]Li Z P, Mu C L, Cui Z J. Critical curves for a fast diffusive polytropic filtration system coupled via nonlinear boundary flux. Z angew
Math Phys, 2009, 60: 284--296
[17]Lieberman G M. Second Order Parabolic Differential Equations. River Edge: World Scientific, 1996
[18] Mi Y S, Mu C L. Critical exponents for a nonlinear degenerate parabolic system coupled via nonlinear boundary flux. submitted
[19]Mi Y S, Mu C L, Chen B T.Critical exponents for a nonlinear degenerate parabolic system coupled via nonlinear boundary flux. J Korean Math Soc (Accepted)
[20]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
[21]Samarskii A A,Galaktionov V A, Kurdyumov S P, Mikhailov A P. Blow-up in Quasilinear Parabolic Equations. Berlin: Walter de Gruyter, 1995
[22]Souplet P. Blow-up in nonlocal reaction-diffusion equations. SIAM J Math Anal, 1998, 29: 1301--1334
[23]Vazquez J L. The Porous Medium Equations: Mathematical Theory. Oxford: Oxford University Press, 2007
[24]Wang M X. The blow-up rates for systems of heat equations with nonlinear boundary conditions. Sci China, 2003, 46A: 169--175
[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 Analysis Applic, 1998, 218: 313--324
[26]Wang S, Xie C H, Wang M X, The blow-up rate for a system of heat equations completely coupled in the boundary conditions. Nonlinear Anal, 1999, 35: 389--398
[27]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
[28]Wu Z Q, Zhao J N, Yin J X, Li H L. Nonlinear Diffusion Equations. River Edge, NJ: World Scientific Publishing Co Inc, 2001
[29]Xiang Z Y, Chen Q, Mu C L. Critical curves for degenerate parabolic equations coupled via non-linear boundary flux. Appl Math Comput, 2007, {\bf 189}: 549--559
[30]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
[31]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
[32] Zhou J, Mu C L. On critical fujita exponents for degenerate parabolic system coupled via nonlinear boundary flux. Pro Edinb Math Soc,
2008, 51: 785--805
[33] Mu C L, Hu X G, Li Y H, Cui Z J. Blow-up and global existence for a coupled system of degenerate parabolic equations in a bounded domain. Acta Mathematica Scientia, 2007, 27B(1): 92--106 |