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arXiv · 2211.05814

Synchronisation for scalar conservation laws via Dirichlet boundary

Ana Djurdjevac·Tommaso Rosati
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Abstract

We provide an elementary proof of geometric synchronisation for scalar conservation laws on a domain with Dirichlet boundary conditions. Unlike previous results, our proof does not rely on a strict maximum principle, and builds instead on a quantitative estimate of the dissipation at the boundary. We identify a coercivity condition under which the estimates are uniform over all initial conditions, via the construction of suitable super- and sub-solutions. In lack of such coercivity our results build on Lp energy estimates and a Lyapunov structure.

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Ana Djurdjevac, Tommaso Rosati. 2022-11-10. Synchronisation for scalar conservation laws via Dirichlet boundary. https://arxiv.org/abs/2211.05814

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