Quenching Behavior for a Nonlinear Parabolic Equation with Nonlinear Boundary Flux

The paper deals with a nonlinear equation in one-dimensional space, of which the nonlinearity appears both in source term and the Neumann boundary condition. Firstly, we proved that the solution of problem (1.1) quenches in finite time and the only quenching point is x = 0 if the initial data is appropriate. Then we established the corresponding quenching rate of the solution.