Reduced Measures Associated with Parabolic Problems

We study the existence and the properties of reduced measures for the parabolic equations $\partial_tu-\Delta u+g(u)=0$ in $\Omega\times(0,\infty)$ subject to the conditions (P): $u=0$ on $\partial\Omega\times(0,\infty)$, $u(x,0)=\mu$ and (P$'$): $u=\mu'$ on $\partial\Omega\times(0,\infty)$, $u(x,0)=0$, where $\mu$ and $\mu'$ are positive Radon measures and $g$ is a continuous nondecreasing function.