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

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”.


35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations