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

Abstract

In this paper, we study porous media equation $u_{t}=\Delta u^{m}-u^{p}$ with nonlinear boundary condition $\frac{\partial u}{\partial\nu}=ku^{q}$. 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.

Keywords

• porous media equation
• nonlinear boundary condition
• bounds for blow-up time