Synchronisation for scalar conservation laws via Dirichlet boundary

Autor:	Djurdjevac, Ana, Rosati, Tommaso
Rok vydání:	2022
Předmět:	Mathematics - Probability Mathematics - Analysis of PDEs 60H15 37H15 37L55 37A25
Druh dokumentu:	Working Paper
Popis:	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. Comment: 21 pages. Comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.05814 Zobrazit plný text záznamu View this record from Arxiv