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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.
We consider a general conservation law on the circle, in the presence of a sublinear damping. If the damping acts on the whole circle, then the solution becomes identically zero in finite time, following the same mechanism as the corresponding ordina
We show the convergence of the zero relaxation limit in systems of $2 times 2$ hyperbolic conservation laws with stochastic initial data. Precisely, solutions converge to a solution of the local equilibrium approximation as the relaxation time tends
We prove the decay of the L 2-distance from the solution u(t) of a hyperbolic scalar conservation law, to some convex, flow-invariant target sets.
A moving mesh discontinuous Galerkin method is presented for the numerical solution of hyperbolic conservation laws. The method is a combination of the discontinuous Galerkin method and the mesh movement strategy which is based on the moving mesh par
We introduce a formulation of the initial and boundary value problem for nonlinear hyperbolic conservation laws posed on a differential manifold endowed with a volume form, possibly with a boundary; in particular, this includes the important case of