The blow-up properties of solutions to semilinear heat equations with nonlinear boundary conditions

摘要

This paper deals with the blow-up properties of solutions to semilinear heat equation u_t - u_(xx) = u~p in (0,1) x (0,T) with the nonlinear boundary conditions u_x(0,t) = 0, u_x(1,t)=u~q on [0,T]. The necessary and sufficient conditions for the solution to have a finite time blow-up and the exact blow-up rates are established. It is also proved that the blow-up will occur only at the boundary x=1.