[1] Filo J. Diffusivity versus absorption through the boundary. J Diff Eqns, 1992, 99: 281--305
[2] Levine H A, Payne L E. Nonexistence theorems for the heat equation with nonlinear boundary conditions and for porous medium equation backward in time. J Diff Eqns, 1974, 16: 319--334
[3] Fujita H. On the blowing up of solutions to the cauchy problems for ut=Δu+u1+α. J Fac Sci Univ Tokyo Sect IA Math, 1996, 13: 109--124
[4] Deng K. The role of critical exponents in blow-up theorems: the sequel. J Math Anal Appl, 2000, 243: 85--126
[5] Quir\'os F, Rossi J D. Blow-up sets and fujita type curves for a degenerate parabolic system with nonlinear boundary conditions.
Indiana Univ Math J, 2001, 50: 629--654
[6] Jin C H, Yin J X. Critical exponents and non-extinction for a fast diffusive polytropic filtration equation with nonlinear boundary sources. Nonlin Anal, 2007, 67: 2217--2223
[7] Pablo A D, Quir\'os F, Rossi J D. Asymptotic simplification for a reaction--diffusion problem with a nonlinear boundary condition.
IMA J Appl Math, 2002, 67: 69--98
[8] Song X F, Zheng S N. Blow-up and blow-up rate for a reaction diffusion model with multiple nonlinearities. Nonlin Anal, 2003, 54: 279--289
[9] Jiang Z X, Zheng S N, Song X F. Blow-up analysis for a nonlinear diffusion equation with nonlinear boundary conditions. Appl Math Lett, 2004, 17: 193--199
[10] Andreu F, Maz\'on J M, Toledo J, Rossi J D. Porous medium equation with absorption and a nonlinear boundary condition. Nonlin Anal, 2002, 49: 541--563
[11] Li Y X, Xie C H. Blow-up for p-Laplacian parabolic equations. Elec J Diff Eqns, 2003, 2003: 1--12
[12] Yin J X, Jin C H. Critical extinction and blow-up exponents for fast diffusive p-Laplacian with sources. Math Meth Appl Sci, 2007, 30: 1147--1167
[13] Li F C, Xie C H. Global and blow-up solutions to a p-Laplacian equation with nonlocal source. Comp Math Appl, 2003, 46: 1525--1533
[14] Ishii H. Asymptotic stability and blowing up of solutions of some nonlinear equations. J Diff Eqns, 1977, 26: 291--319
[15] Levine H A, Payne L E. Nonexistence of global weak solutions of classes of nonlinear wave and parabolic equations. J Math Anal Appl, 1976, 55: 329--334
[16] Tsutsumi M. Existence and nonexistence of global solutions for nonlinear parabolic equations. Publ Res Inst Math Sci, 1972, 8: 221--229
[17] Zhao J. Existence and nonexistence of solutions for ut- {\rm div}(|\nabla u|^{p-2}\nabla u) = f(\nabla u, x, t). J Math Anal Appl, 1993, 172: 130--146
[18] Ladyzenskaja O A, Uralceva N N. Linear and Quasilinear Equations of Elliptic Type. Moscow: Nauka, 1973
[19] Wu Z Q, Zhao J N, Yin J X, Li H L. Nonlinear Diffusion Equations. Singapore: World Scientific, 2001 |