Disappearance of interfaces for the porous medium equation with variable density and absorption
Guillermo Reyes, Ariel Sánchez · Asymptotic Analysis · 2003
We improve previous results on the qualitative properties of solutions to the Cauchy problem for the equation ρ(x)u t =(u m ) xx −c 0 u p , where 1 0 >0 with nonnegative, compactly supported initial data. Precisely, we prove that if the density ρ(x) decays faster than |x| −k with k>k * =2(p−1)/(p−m), then the interfaces disappear in finite time for any initial data in the above class. We also weaken conditions previously imposed on the density function.