GLOBAL ENTROPY SOLUTIONS IN L∞ TO THE EULER EQUATIONS AND EULER-POISSON EQUATIONS FOR ISOTHERMAL FLUIDS WITH SPHERICAL SYMMETRY ∗ GUI-QIANG CHEN† AND TIAN-HONG LI† Abstract. We prove the existence of global entropy solutions in L∞ to the multidimensional Euler equations and Euler-Poisson equations for compressible isothermal fluids with spherically symmetric initial data that allows vacuum and ...

We discuss numerical stabilisation of dynamics governed by nonlinear hyperbolic conservation laws through feedback boundary conditions. Using a discrete Lyapunov function we prove exponential decay of the discrete solution to first– order finite volume schemes in conservative form. Decay rates are established for a large class of finite volume schemes including the Lax–Friedrichs scheme. Theore...

The aim of this paper is to investigate the stability of boundary layers which appear in numerical solutions of hyperbolic systems of conservation laws in one space dimension on regular meshes. We prove stability under a size condition for Lax Friedrichs type scheme and inconditionnal stability in the scalar case. Examples of unstable boundary layers are also given.

One cycle of a composite finite difference scheme is defined as several time steps of an oscillatory scheme such as Lax–Wendroff followed by one step of a diffusive scheme such as Lax–Friedrichs. We apply this idea to gas dynamics in Lagrangian coordinates. We show numerical results in two dimensions for Noh’s infinite strength shock problem and the Sedov blast wave problem, and for several one...

We prove the well-posedness of entropy weak solutions of a scalar conservation law with non-local flux arising in traffic flow modeling. The result is obtained providing accurate L∞, BV and L estimates for the sequence of approximate solutions constructed by an adapted Lax-Friedrichs scheme.

A convergence theorem for the vanishing viscosity method and for the Lax–Friedrichs schemes, applied to a nonstrictly hyperbolic and nongenuinely nonlinear system is established. Using the theory of compensated compactness we prove convergence of a subsequence in the strong topology. c © 1999 Elsevier Science B.V. All rights reserved.

We establish the global existence of L∞ solutions for a model of polytropic gas flow with diffusive entropy. The result is obtained by showing the convergence of a class of finite difference schemes, which includes the Lax– Friedrichs and Godunov schemes. Such convergence is achieved by proving the estimates required for the application of the compensated compactness theory.