Blow-up solutions and global solutions for nonlinear parabolic equations with mixed boundary conditions

This paper deals with the blow-up of positive solutions for a nonlinear parabolic equation subject to mixed boundary condition. We obtain the conditions under which the solutions may exist globally or blow up in a finite time by a new approach. Moreover, upper estimates of “blow-up time”, blow-up rate and global solutions are obtained also. The results improve and extend importantly the findings obtained by A. Friedman and R. Sperb.