Existence of solutions to the parabolic equation with a singular potential of the sobolev-hardy type

We study the existence of solutions to the following parabolic equation equation(P){ut−Δpu=λ|x|2|u|q−2u,(x, t) ∈ Ω × (0, ∞),u(x, 0)=f(x),x ∈ Ωu(x, t)=0,(x, t) ∈∂Ω × (0, ∞) where −Δpu≡−div(|∇u|p−2∇u), 1