Enache C. Blow-up phenomena for a class of quasilinear parabolic problems under Robin boundary conditions[J]. Appl Math Lett,2011,24:288-292.
[2]
Enache E. Lower bounds for blow-up time in some non-linear parabolic problems under Neumann boundary conditions[J]. Glasgow Math J,2011,53:569-575.
[3]
Payne L E, Philippin G A. Blow-up in a class of non-linear parabolic problems with time-dependent coefficients under Robin type boundary conditions[J]. Appl Anal,2012,91:2245-2256
[4]
Payne L E, Song J C. Lower bounds for blow-up time in a nonlinear parabolic problem[J]. J Math Anal Appl,2009,354:394-396.
[5]
Payne L E, Schaefer P W. Blow-up phenomena for some nonlinear parabolic systems[J]. Int J Pure Appl Math,2008,48:193-202.
[6]
Payne L E, Song J C. Blow-up and decay criteria for a model of chemotaxis[J]. J Math Anal Appl,2010,367:1-6.
Ball J M. Remarks on blow-up and nonexistence theorems for nonlinear evolution equations[J]. Quart J Math Oxford,1977,28:473-486.
[10]
Kielhofer H. Existenz und Regularitiat von Lsungen semilinearer parabolischer Anfangs-Randwertprobleme[J]. Math Z,1975,142:131-160.
[11]
Straughan B. Explosive Instabilities in Mechanics[M]. Berlin:Springer-Verlag,1998.
[12]
Quittner R, Souplet P. Superlinear Parabolic Problems Blow-up, Global Existence and Steady States[M]. Basel:Birkhauser,2007.
[13]
Levine H A. Nonexistence of global weak solutions to some properly and improperly posed problems of mathematical physics: The method of unbounded Fourier coefficients[J]. Math Ann,1975,214:205-220.
[14]
Galaktionov V A, Vazquez J L. The problem of blow-up in nonlinear parabolic equations[J]. Discrete Cont Dyn Syst,2002,8(2):399-433.
[15]
Payne L E, Schaefer P W. Lower bounds for blow-up time in parabolic problems under Dirichlet conditions[J]. J Math Anal Appl,2007,328:1196-1205.
[16]
Payne L E, Schaefer P W. Lower bounds for blow-up time in parabolic problems under Neumann conditions[J]. Appl Anal,2006,85:1301-1311.
[17]
Payne L E, Schaefer P W. Blow-up phenomena for some nonlinear parabolic problems[J]. Appl Anal,2008,87:699-707.
[18]
Payne L E, Schaefer P W. Bounds for the blow-up time for heat equation under nonlinear boundary condition[J]. Proc Roy Soc Edin,2009,A139:1289-1296.
[19]
Payne L E, Philippin G A, Vernier Piro S. Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition I[J]. Z Angew Math Phys,2010,61:999-1007.
[20]
Chen S. Global existence and blow-up of solutions for a parabolic equation with a gradient term[J]. Proc Am Math Soc,2001,129:975-981.
[21]
Payne L E, Philippin G A, Schaefer P W. Bounds for blow-up time in nonlinear parabolic problems[J]. J Math Anal Appl,2008,338:438-447.
[22]
Payne L E, Philippin G A, Vernier Piro S. Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition II[J]. Nonlinear Anal,2010,73:971-978.
[23]
Payne L E, Philippin G A, Schaefer P W. Blow-up phenomena for some nonlinear parabolic problems[J]. Nonlinear Anal,2008,69:3495-3502.
[24]
Payne L E, Schaefer P W. Lower bounds for blow-up time in parabolic problems under Dirichlet conditions[J]. J Math Anal Appl,2007,328:1196-1205.