| [1] Wu Z Q, Zhao J N, Yin J X, Li H L. Nonlinear Diffusion Equations. River Edge, NJ: World Scientific Publishing, 2001
[2] Chipot M, Weissler F B. Some blow-up results for a nonlinear parabolic problem with a gradient term. SIAM J Math Anal, 1989, 20: 886-907
[3] Souplet P. Finite time blowup for a nonlinear parabolic equation with a gradient term and applications. Math Methods Appl Sci, 1996, 19: 1317-1333
[4] Layne L E, Schaefer P W. Lower bounds for blow-up time in parabolic problems under Dirichlet conditions. J Math Anal Appl, 2007, 328: 1196-1205
[5] Payne L E, Philippin G A, Schaefer P W. Bounds for blow-up time in nonlinear parabolic problems. J Math Anal Appl, 2008, 338: 438-447
[6] Payne L E, Philippin G A, Schaefer P W. Blow-up phenomena for some nonlinear parabolic problems. Nonlinear Anal, 2008, 69: 3495-3502
[7] Lv X S, Song X F. Bounds of blowup time in parabolic equations with weighted source under nonhomogeneous Neumann boundary condition. Math Math Appl Sci, 2014, 37: 1019-1028
[8] Song X F, Lv X S. Bounds of blowup time and blowup rate estimates for a type of parabolic equations with weighted source. Appl Math Computation, 2014, 236: 78-92
[9] Tang G S, Li Y F, Yang X. Lower bounds for the blow-up time of the nonlinear non-local reaction diffusion problems in RN (N≥3). Boundary Value Problems, 2014, 2014: 265
[10] Zhao J N. Existence and noexistence of solutions for ut=div(|▽u|p-2▽u)+f(▽u, u, x, t). J Math Anal Appl, 1993, 172: 130-146
[11] Talenti G. Beat constant in Sobolev inequality. Ann Math Pure Appl, 1976, 110: 353-372 |