Maximum principle for nonlinear parabolic equations

A maximum principle is obtained for solutions of parabolic equations of the form
$$ {\mathcal L} u - u_t = f (x, t, u, D u), $$
where
$$ {\mathcal L} u = \sum_{i,j=1}^n a_{ij} (x, t, u) \frac{\partial^2 u}{\partial x_i \partial x_j} + \sum_{i=1}^n b_i (x, t, u) \frac{\partial u}{\partial x_i}. $$