Gagneux, Gérard; Madaune-Tort, Monique On the uniqueness of weak solutions for nonlinear diffusion-convection processes. (Unicité des solutions faibles d’équations de diffusion-convection.) (French. Abridged English version) Zbl 0826.35057 C. R. Acad. Sci., Paris, Sér. I 318, No. 10, 919-924 (1994). The authors’ abstract: “This note treats the uniqueness question for Cauchy-Dirichlet problems connected to a scalar \(n\)-dimensional conservation law: \[ u_t - \Delta \varphi (u) - \text{div} \bigl( \psi (u)G \bigr) = 0. \] The continuity of the function \(\psi \circ \varphi^{-1}\) in fact ensures that every weak solution is a Kruskov solution, namely satisfies implicitly an entropy condition; taking just into consideration this relevant property, we prove a global uniqueness result for non-smooth initial data”. Reviewer: S.Eloshvili (Tbilisi) Cited in 13 Documents MSC: 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35K20 Initial-boundary value problems for second-order parabolic equations Keywords:nonlinear diffusion-convection processes; Kruskov solution PDFBibTeX XMLCite \textit{G. Gagneux} and \textit{M. Madaune-Tort}, C. R. Acad. Sci., Paris, Sér. I 318, No. 10, 919--924 (1994; Zbl 0826.35057)