On the Rate of Convergence to Equilibrium for a System of Conservation Laws including a Relaxation Term
نویسندگان
چکیده
We analyze a simple system of conservation laws with a strong relaxation term. Well-posedness of the Cauchy problem, in the framework of BV-solutions, is proved. Furthermore, we prove that the solutions converge towards the solution of an equilibrium model as the relaxation time > 0 tends to zero. Finally, we show that the dierence between an equilibrium solution (= 0) and a non-equilibrium solution (> 0), measured in L 1 , is bounded by O(1=3).
منابع مشابه
A system of conservation laws including a sti relaxation term ; the 2 D case
We analyze a system of conservation laws in two space dimensions with stii relaxation terms. A semi-implicit nite diierence method approximating the system is studied and an error bound of order O(p t) measured in L 1 is derived. This error bound is independent of the relaxation time > 0. Furthermore, it is proved that the solutions of the system converge towards the solutions of the equilibriu...
متن کاملAn L1{error Bound for a Semiimplicit Difference Scheme Applied to a Stiff System of Conservation Laws
A straightforward semi-implicit nite diierence method approximating a system of conservation laws including a stii relaxation term is analyzed. We show that the error, measured in L 1 , is bounded by O(p t) independent of the stiiness, where the time step t represents the mesh size. As a simple corollary we obtain that solutions of the stii system converge towards the solution of an equilibrium...
متن کاملOn the Zero Relaxation Limit for a System Modeling the Motions of a Viscoelastic Solid∗
We consider a simple model of the motions of a viscoelastic solid. The model consists of a two-by-two system of conservation laws including a strong relaxation term. We establish the existence of a BV-solution of this system for any positive value of the relaxation parameter. We also show that this solution is stable with respect to the perturbations of the initial data in L1. By deriving the u...
متن کاملConvergence to Equilibriumfor the Relaxation Approximations of Conservation Laws
We study the Cauchy problem for 22 semilinear and quasilinear hyperbolic systems with a singular relaxation term. Special comparison and compactness properties are established by assuming the subcharacteristic condition. Therefore we can prove the convergence to equilibrium of the solutions of these problems as the singular perturbation parameter tends to zero. This research was strongly motiva...
متن کاملDiffusive Relaxation 3× 3 Model for a System of Viscoelasticity
In this paper we study the global existence and the relaxation limit for a 3 × 3 hyperbolic system of conservation laws with sublinear relaxation term. In particular, the convergence for solutions in Sobolev spaces toward the solutions to the equilibrium system, which is a 2×2 degenerate parabolic system, is proved. This is the first example of a semilinear relaxation approximation for a degene...
متن کامل