Finite speed of propagation for the porous media equation with lower order terms (Q1576896)

This paper is devoted to the finite speed of propagation of positive solutions of the Cauchy-Dirichlet problem for the porous media equation with absortion term \[ \begin{cases} \frac{\partial u}{\partial t}=\Delta u^m-u^p & \text{in }\Omega\times (0,T),\\ u(x,t)=0 & \text{on }\partial \Omega\times (0,T),\\ u(x,0)=u_0(x) & \text{on }\Omega,\end{cases} \] where \(p>1\), \(m>1\), \(\Omega-\mathbb{R}^N\cap \{x_1,\dots,x_k>0\}\), \(k\in[1,N]\) and \(u_0\geq 0\) with compact support. The authors present new upper bounds of the free boundary.