We study the blow-up behavior of solutions of the semilinear heat equations under the Dirichlet boundary condition or the Neumann boundary condition. We prove the nondegeneracy of blow-up of the solutions. Furthermore, we give a result on the blow-up rate of the solutions under the Neumann boundary condition.
"Blow-up behavior for semilinear heat equations with boundary conditions." Differential Integral Equations 16 (6) 663 - 690, 2003.