Abstract
This paper deals with the blow-up properties of solutions to semilinear heat equation ut – uxx = up in (0, 1) × (0, T) with the Neumann boundary condition ux (0, t)= 0, ux(1, t) = 1 on [0, T). The necessary and sufficient conditions under which all solutions to have a finite time blow-up and the exact blow-up rates are established. It is proved that the blow-up will occur only at the boundary x = 1. The asymptotic behavior near the blow-up time is also studied.
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