Renormalized solutions to nonlinear parabolic problems with blowing up coefficients and general measure data

An existence result is established for a class of quasilinear parabolic problem which is a diffusion type equations having continuous coefficients blowing up for a finite value of the unknown, a second hand μ∈Mb(Q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu \in \mathcal {M}_{b}(Q)$$\end{document} and an initial data u0∈L1(Ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_{0}\in L^{1}(\Omega )$$\end{document}. We develop a technique which relies on the notion of a renormalized solution and an adequate regularization in time for certain truncation functions. Some compactness results are also shown under additional hypotheses.