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Let $\Omega $ be a bounded domain of $\mathbb{R}^{N}(N\geq 2)$. We obtain anecessary and a sufficient condition, expressed in terms of capacities, forexistence of a solution to the porous medium equation with absorption\begin{equation*} \left\{ \begin{array}{l} {u_{t}}-{\Delta}(|u|^{m-1}u)+|u|^{q-1}u=\mu ~ \text{in }\Omega \times (0,T), \\{u}=0~~~\text{on }\partial \Omega \times (0,T), \\ u(0)=\sigma , \end{array}\right. \end{equation*} where $\sigma$ and $\mu$ are bounded Radon measures,$q>\max (m,1)$, $m>\frac{N-2}{N}$. We also obtain a sufficient condition forexistence of a solution to the $p$-Laplace evolution equation \begin{equation*}\left\{ \begin{array}{l} {u_{t}}-{\Delta _{p}}u+|u|^{q-1}u=\mu ~~\text{in}\Omega \times (0,T), \\ {u}=0 ~ \text{on }\partial \Omega \times (0,T), \\u(0)=\sigma . \end{array} \right. \end{equation*} where $q>p-1$ and $p>2$.

Pointwise estimates and existence of solutions of porous medium and $p$-Laplace evolution equations with absorption and measure data