Blowup rate for heat equation in Lipschitz domains with nonlinear heat source terms on the boundary

This paper establishes the blowup rate estimate near the blowup time for the heat equation ut = Δu with the nonlinear boundary condition un = up on the boundary ∂Ω × [0,T ) for a bounded Lipschitz domain and for the nonlinear boundary condition un = exp(u) on the boundary for a two-dimensional disc with nonradially symmetric data.