2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213033We consider the long-time behavior of the entropy solution of a first-order scalar conservation law on a Riemannian manifold. In the case of the Torus, we show that, under a weak property of genuine non-linearity of the flux, the solution converges to its average value in $L^{p}$, $1\leq p<+\infty$. We give a partial result in the general case.Analysis of PDEs35L65, 35B40text