Let Ω be a bounded domain of RN, and Q=Ω×(0,T). We consider problems\textit{ }of the type % \left\{
\begin{array} [c]{l}% {u_{t}}-{\Delta_{p}}u\pm\mathcal{G}(u)=\mu\qquad\text{in
}Q,\\ {u}=0\qquad\text{on }\partial\Omega\times(0,T),\\
u(0)=u_{0}\qquad\text{in }\Omega, \end{array} \right. where Δp
is the p-Laplacian, μ is a bounded Radon measure, u0∈L1(Ω), and ±G(u) is an absorption or a source term. In
the model case G(u)=±∣u∣q−1u(q>p−1),
or G has an exponential type. We prove the existence of
renormalized solutions for any measure μ in the subcritical case, and give
sufficient conditions for existence in the general case, when μ is good in
time and satisfies suitable capacitary conditions.Comment: arXiv admin note: substantial text overlap with arXiv:1310.525