Quasi-static limit for a hyperbolic conservation law

We study the quasi-static limit for the L-infinity 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.

Automated summary

The study focuses on the quasi-static limit of scalar one-dimensional hyperbolic equations with strictly concave or convex flux and time dependent boundary conditions. It shows that the quasi-stationary profile evolves with the quasi-static equation, and its entropy solution is determined by the stationary profile corresponding to the boundary data at a given time.