Existence of solutions for a class of porous medium type equations with L1L1 data

In this paper, we study a class of degenerate parabolic equations of porous medium-type with a lower order term and L1L1 data, i.e.  ∂u∂t−div(a(x,t,u,∇u))+F(x,t,u,∇u)=f, where the principal part of the operator is degenerate in u=0u=0. Under some hypothesis on aa and FF, we prove that the problem admits at least a renormalized solution.