Blanchard, Dominique; Redwane, Hicham Renormalized solutions of doubly nonlinear parabolic equations. (Solutions renormalisées d’équations paraboliques à deux non linéarités.) (French. Abridged English version) Zbl 0810.35038 C. R. Acad. Sci., Paris, Sér. I 319, No. 8, 831-835 (1994). Results about existence, uniqueness and comparison are established for renormalized solutions of the following class of doubly nonlinear parabolic initial boundary value problems: \[ \partial_ t b(u)- \Delta u+ \text{div } \Phi(u)=f \quad \text{in } \Omega\times (0,T), \]\[ u=0 \quad \text{on } \partial\Omega\times (0,T), \qquad b(u)|_{t=0} =b(u_ 0) \quad \text{in } \Omega. \] Here \(\Omega\subset \mathbb{R}^ N\) is bounded and open, \(b\) is a strictly increasing \(C^ 1\)-function on an open interval \(I\) with \(b(I)= \mathbb{R}\) and \(b(0)=0\), \(b^{-1}: \mathbb{R}\to I\) and \(\Phi: \mathbb{R}\to \mathbb{R}^ N\) are continuous, \(u_ 0\) is a measurable function such that \(b(u_ 0)\in L^ 1(\Omega)\), and \(f\in L^ 1(\Omega\times (0,T))\). Reviewer: L.Recke (Berlin) Cited in 12 Documents MSC: 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35D05 Existence of generalized solutions of PDE (MSC2000) 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:doubly nonlinear parabolic initial boundary value problems PDFBibTeX XMLCite \textit{D. Blanchard} and \textit{H. Redwane}, C. R. Acad. Sci., Paris, Sér. I 319, No. 8, 831--835 (1994; Zbl 0810.35038)