Quasi-static limit for a hyperbolic conservation law

11 Mar 2021 · Stefano Marchesani, Stefano Olla, Lu Xu ·

We study the quasi-static limit for the $L^\infty$ entropy weak solution of scalar one-dimensional hyperbolic equations with strictly concave or convex flux and time dependent boundary conditions. The quasi-stationary profile evolves with the quasi-static equation, whose entropy solution is determined by the stationary profile corresponding to the boundary data at a given time.