Compactness properties of the generalized green operator associated to the porous-media equation

Abstract

We show some compactness properties of the operator f--u, where u is the solution of the nonlinear diffusion equation ut−Δφ(u)=f on (0,T)×Ω associated with the parabolic boundary conditions φ(u)=0 on (0,T)×∂Ω and u(0,⋅)=u0(⋅) on Ω, u0 a given function in L1(Ω). Our results are carried out under the general assumption that φ is a real continuous strictly increasing function satisfying φ(0)=0.