## 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”.

### MSC:

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