Convergence to Equilibriumfor the Relaxation Approximations of Conservation Laws
نویسنده
چکیده
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 motivated by the recent numerical investigations of S. Jin and Z. Xin on the relaxation schemes for conservation laws.
منابع مشابه
Stability and Convergence of Relaxation Schemes to Hyperbolic Balance Laws via a Wave Operator
This article deals with relaxation approximations of nonlinear systems of hyperbolic balance laws. We introduce a class of relaxation schemes and establish their stability and convergence to the solution of hyperbolic balance laws before the formation of shocks, provided that we are within the framework of the compensated compactness method. Our analysis treats systems of hyperbolic balance law...
متن کاملDiscrete Kinetic Schemes for Multidimensional Systems of Conservation Laws
We present here some numerical schemes for general multidimensional systems of conservation laws based on a class of discrete kinetic approximations, which includes the relaxation schemes by S. Jin and Z. Xin. These schemes have a simple formulation even in the multidimensional case and do not need the solution of the local Riemann problems. For these approximations we give a suitable multidime...
متن کاملMaterials with Internal Variables and Relaxation to Conservation Laws
The theory of materials with internal state variables of Coleman and Gurtin CG] provides a natural framework to investigate the structure of relaxation approximations of conservation laws from the viewpoint of continuum thermomechanics. After reviewing the requirements imposed on constitutive theories by the principle of consistency with the Clausius-Duhem inequality, we pursue two speciic theo...
متن کاملConvergence and Error Estimates of Relaxation Schemes for Multidimensional Conservation Laws
M. A. Katsoulakis, G. Kossioris and Ch. Makridakis Abstract. We study discrete and semidiscrete relaxation schemes for multidimensional scalar conservation laws. We show convergence of the relaxation schemes to the entropy solution of the conservation law and derive error estimates that exhibit the precise interaction between the relaxation time and the space/time discretization parameters of t...
متن کاملConvergence of Relaxation Schemes for Conservation Laws
We study the stability and the convergence for a class of relaxing numerical schemes for conservation laws. Following the approach recently proposed by S. Jin and Z. Xin, we use a semilinear local relaxation approximation, with a stii lower order term, and we construct some numerical rst and second order accurate algorithms, which are uniformly bounded in the L 1 and BV norms with respect to th...
متن کامل