Electronic Journal of Qualitative Theory of Differential Equations (Feb 2021)
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.
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