Very weak solutions of singular porous medium equations with measure data

We consider non-homogeneous, singular (0 < m < 1) porous medium type equations with a non-negative Radon-measure having finite total mass \mu(E_T) on the right-hand side. We deal with a Cauchy-Dirichlet problem for these type of equations, with homogeneous boundary conditions on the parabolic boundary of the domain E_T, and we establish the existence of a solution in the sense of distributions. Finally, we show that the constructed solution satises linear pointwise estimates via linear Riesz potentials.