The quenching behavior of a nonlinear parabolic equation with nonlinear boundary outflux

In this paper we are concerned with the quenching behavior of a nonlinear parabolic problem in one-dimensional space, of which the nonlinearity appears both in source term and in Neumann boundary condition. First we proved that the solution quenches only on the left boundary in finite time if the given initial datum is monotone. Then we give the estimate for the quenching rate of the solution near the quenching time.