1 |
S. Wang, C. H. Xie, and M. X. Wang, The blow-up rate for a system of heat equations completely coupled in the boundary conditions, Nonlinear Anal. 35 (1999), no. 3, Ser. A: Theory Methods, 389-398.
DOI
ScienceOn
|
2 |
A. V. Ivanov, Holder estimates for quasilinear doubly degenerate parabolic equations, J. Soviet Math. 56 (1991), no. 2, 2320-2347.
DOI
|
3 |
Z. X. Jiang and S. N. Zheng, Doubly degenerate paralolic equation with nonlinear inner sources or boundary flux, Doctor Thesis, Dalian University of Tcchnology, In China, 2009
|
4 |
C. H. Jin and J. X. Yin, Critical exponents and non-extinction for a fast diffusive polytropic filtration equation with nonlinear boundary sources, Nonlinear Anal. 67 (2007), no. 7, 2217-2223.
DOI
ScienceOn
|
5 |
A. S. Kalashnikov, A nonlinear equation arising in the theory of nonlinear filtration, Trudy Sem. Petrovsk. No. 4 (1978), 137-146.
|
6 |
A. S. Kalashnikov, Some problems of the qualitative theory of second-order nonlinear degenerate parabolic equations, Uspekhi Mat. Nauk 42 (1987), no. 2(254), 135-176, 287.
|
7 |
K. A. Lee, A. Petrosyan, and J. L. Vazquez, Large-time geometric properties of solutions of the evolution p-Laplacian equation, J. Differential Equations 229 (2006), no. 2, 389-411.
DOI
ScienceOn
|
8 |
H. A. Levine, The role of critical exponents in blowup theorems, SIAM Rev. 32 (1990), no. 2, 262-288.
DOI
ScienceOn
|
9 |
Z. P. Li and C. L. Mu, Critical exponents for a fast diffusive polytropic filtration equation with nonlinear boundary flux, J. Math. Anal. Appl. 346 (2008), no. 1, 55-64.
DOI
ScienceOn
|
10 |
Z. P. Li and C. L. Mu, Critical curves for fast diffusive non-Newtonian equations coupled via nonlinear boundary flux, J. Math. Anal. Appl. 340 (2008), no. 2, 876-883.
DOI
ScienceOn
|
11 |
Z. P. Li, C.L. Mu, and Z. J. Cui, Critical curves for a fast diffusive polytropic filtration system coupled via nonlinear boundary flux, Z. Angew. Math. Phys. 60 (2009), no. 2, 284-298.
DOI
|
12 |
G. Astrita and G. Marrucci, Principles of Non-Newtonian Fluid Mechanics, McGraw-Hill, New York, 1974.
|
13 |
Z. J. Cui, Critical curves of the non-Newtonian polytropic filtration equations coupled with nonlinear boundary conditions, Nonlinear Anal. 68 (2008), no. 10, 3201-3208.
DOI
ScienceOn
|
14 |
K. Deng and H. A. Levine, The role of critical exponents in blow-up theorems: the sequel, J. Math. Anal. Appl. 243 (2000), no. 1, 85-126.
DOI
ScienceOn
|
15 |
E. Dibenedetto, Degenerate Parabolic Equations, Springer-Verlag, Berlin, New York, 1993.
|
16 |
R. Ferreira, A. de Pablo, F. Quiros, and J. D. Rossi, The blow-up profile for a fast diffusion equation with a nonlinear boundary condition, Rocky Mountain J. Math. 33 (2003), no. 1, 123-146.
DOI
ScienceOn
|
17 |
H. Fujita, On the blowing up of solutions of the Cauchy problem for ut = , J. Fac. Sci. Univ. Tokyo Sect. I 13 (1966), 109-124.
|
18 |
V. A. Galaktionov and H. A. Levine, A general approach to critical Fujita exponents in nonlinear parabolic problems, Nonlinear Anal. 34 (1998), no. 7, 1005-1027.
DOI
ScienceOn
|
19 |
V. A. Galaktionov and H. A. Levine, On critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary, Israel J. Math. 94 (1996), 125-146.
DOI
|
20 |
Z. J. Wang, J. X. Yin, and C. P. Wang, Critical exponents of the non-Newtonian polytropic filtration equation with nonlinear boundary condition, Appl. Math. Lett. 20 (2007), no. 2, 142-147.
DOI
ScienceOn
|
21 |
Z. Q. Wu, J. N. Zhao, J. X. Yin, and H. L. Li, Nonlinear Diffusion Equations, World Scientific Publishing Co. Inc. River Edge, NJ, 2001.
|
22 |
Z. Y. Xiang, Q. Chen, and C. L. Mu, Critical curves for degenerate parabolic equations coupled via non-linear boundary flux, Appl. Math. Comput. 189 (2007), no. 1, 549-559.
DOI
ScienceOn
|
23 |
S. N. Zheng, X. F. Song, and Z. X. Jiang, Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux, J. Math. Anal. Appl. 298 (2004), no. 1, 308-324.
DOI
ScienceOn
|
24 |
J. Zhou and C. L. Mu, The critical curve for a non-Newtonian polytropic filtration system coupled via nonlinear boundary flux, Nonlinear Anal. 68 (2008), no. 1, 1-11.
DOI
ScienceOn
|
25 |
J. Zhou and C. L. Mu, On the critical Fujita exponent for a degenerate parabolic system coupled via nonlinear boundary flux, Proc. Edinb. Math. Soc. (2) 51 (2008), no. 3, 785-805.
DOI
ScienceOn
|
26 |
M. Pedersen and Z. G. Lin, Blow-up analysis for a system of heat equations coupled through a nonlinear boundary condition, Appl. Math. Lett. 14 (2001), no. 2, 171-176.
DOI
ScienceOn
|
27 |
G. M. Lieberman, Second Order Parabolic Differential Equations, World Scientific Publishing Co., Inc., River Edge, NJ, 1996.
|
28 |
Z. G. Lin, Blowup behaviors for diffusion system coupled through nonlinear boundary conditions in a half space, Sci. China Ser. A 47 (2004), no. 1, 72-82.
DOI
|
29 |
Y. S. Mi and C. L. Mu, Critical exponents for a nonlinear degenerate parabolic system coupled via nonlinear boundary flux, submitted.
|
30 |
F. Quiros 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), no. 1, 629-654.
DOI
|
31 |
A. A. Samarskii, V. A. Galaktionov, S. P. Kurdyumov, and A. P. Mikhailov, Blow-up in Quasilinear Parabolic Equations, Walter de Gruyter, Berlin, 1995.
|
32 |
P. Souplet, Blow-up in nonlocal reaction-diffusion equations, SIAM J. Math. Anal. 29 (1998), no. 6, 1301-1334.
DOI
ScienceOn
|
33 |
J. L. Vazquez, The Porous Medium Equations: Mathematical Theory, Oxford University Press, Oxford, 2007.
|
34 |
M. X. Wang, The blow-up rates for systems of heat equations with nonlinear boundary conditions, Sci. China Ser. A 46 (2003), no. 2, 169-175.
DOI
|
35 |
S. Wang, C. H. Xie, and M. X. Wang, Note on critical exponents for a system of heat equations coupled in the boundary conditions, J. Math. Anal. Appl. 218 (1998), no. 1, 313-324.
DOI
ScienceOn
|