A note on gradient blowup rate of the inhomogeneous hamilton-jacobi equations

The gradient blowup of the equation ut = Δu + a(x)|∇u|p + h(x), where p > 2, is studied. It is shown that the gradient blowup rate will never match that of the self-similar variables. The exact blowup rate for radial solutions is established under the assumptions on the initial data so that the solution is monotonically increasing in time.