The profile near blowup time for solution of the heat equation with a nonlinear boundary condition

Source abstract

This paper studies the blowup profile near the blowup time for the heat equation u t = Δ u {u_t} = \Delta u with the nonlinear boundary condition u n = u p {u_n} = {u^p} on ∂ Ω × [ 0 , T ) \partial \Omega \times [0,T) . Under certain assumptions, the exact rate of the blowup is established. It is also proved that the blowup will not occur in the interior of the domain. The asymptotic behavior near the blowup point is also studied.