论文信息 - Bounds for blow-up time for the heat equation under nonlinear boundary conditions

Bounds for blow-up time for the heat equation under nonlinear boundary conditions

A differential inequality technique is used to determine a lower bound on the blow-up time for solutions to the heat equation subject to a nonlinear boundary condition when blow-up of the solution does occur. In addition, a sufficient condition which implies that blow-up does occur is determined.

P. W. Schaefer | L. Payne | P. Schaefer | L. E. Payne

[1] Lawrence E. Payne,et al. Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time , 1974 .

[2] Lawrence E. Payne,et al. Lower bounds for blow-up time in parabolic problems under Dirichlet conditions , 2007 .

[3] Howard A. Levine,et al. Nonexistence of global weak solutions to some properly and improperly posed problems of mathematical physics: The method of unbounded fourier coefficients , 1975 .

[4] Gérard A. Philippin,et al. Blow-up phenomena for some nonlinear parabolic problems , 2008 .

[5] A. P. Mikhailov,et al. Blow-Up in Quasilinear Parabolic Equations , 1995 .

[6] Brian Straughan,et al. Explosive Instabilities in Mechanics , 1998 .

[7] Lawrence E. Payne,et al. Lower bounds for blow-up time in parabolic problems under Neumann conditions , 2006 .

[8] Gérard A. Philippin,et al. Bounds for blow-up time in nonlinear parabolic problems , 2008 .

[9] Hermann Brunner,et al. Blowup in diffusion equations: a survey , 1998 .

[10] A. Carvalho,et al. Parabolic problems with nonlinear boundary conditions and critical nonlinearities , 1999 .

[11] Victor A. Galaktionov,et al. The problem of blow-up in nonlinear parabolic equations , 2002 .