Blow-up of solutions for a class of semilinear reaction diffusion equations with mixed boundary conditions

Abstract

The Hopf's maximum principles are utilized to deal with the problem on blow-up of the solutions for a class of semilinear reaction diffusion equations u, t = Δ u + f( x, u, q, t) ( q = |▽ u| 2), subject to mixed boundary conditions. Some nonexistence theorems of global solutions and the bounds of “blow-up time” are obtained.