Finite speed of propagation for the porous media equation with lower order terms
Salvatore Bonafede, Giuseppa Rita Cirmi, Anatoli Fedorovich Tedeev · Discrete and Continuous Dynamical Systems · 2000
We study the finite speed of propagation of the Cauchy-Dirichlet problem for theporous media equation with absorption or convection terms in the strip $\mathfrak R_k^N\times (0,T)$,where $\mathfrak R_k^N=\mathfrak R^N\cap\{x_1, ..., x_k>0\}$,$1\leq k\leq N $ and we find new upper bounds of thefree boundary.Finally, we consider the case of higher order parabolic equations.