On the notion of renormalized solution to nonlinear parabolic equations with general measure data

Abstract

Here we introduce a new notion of renormalized solution to nonlinear parabolic problems with general measure data whose model is $$\{\begin{array}{llcc}{u}_t-{\Delta }_{p}u=\mu & \text{in}(0,T)\times \Omega ,u=u_0& \text{on}\{0\}\times \Omega ,u=0& \text{on}(0,T)\times \partial \Omega ,\end{array}$$ for any, possibly singular, nonnegative bounded measure $\mu$. We prove existence of such a solutions and we discuss their main properties.