The Interfaces of an Inhomogeneous Porous Medium Equation with Convection
Raúl Ferreira, Arturo de Pablo, Guillermo Reyes, Ariel Sánchez · Communications in Partial Differential Equations · 2006
We study the evolution of the interfaces of solutions to the nonhomogeneous porous medium equation with convection with n, m > 1, and ρ(x) > 0, ρ(x) → 0 as |x|→∞. We characterize when the interfaces go to ±infin; in finite time in terms of ρ. Since the equation is not symmetric, the left and right interfaces behave in a completely different way. Moreover, their behaviour strongly departs from the purely diffusive case.