Blow-up analysis for a porous media equation with nonlinear sink and nonlinear boundary condition

In this paper, we study porous media equation ut = ∆u m − u p with nonlinear boundary condition ∂u ∂ν = kuq . We determine some sufficient conditions for the occurrence of finite time blow-up or global existence. Moreover, lower and upper bounds for blow-up time are also derived by using various inequality techniques