Vanishing Viscosity Limit for Initial-Boundary Value Problems for Conservation Laws
نویسندگان
چکیده
The convergence of the vanishing viscosity method for initialboundary value problems is analyzed for nonlinear hyperbolic conservation laws through several representative systems. Some techniques are developed to construct the global viscous solutions and establish the H−1 compactness of entropy dissipation measures for the convergence of the viscous solutions with general initial-boundary conditions. The representative examples considered include the systems of isentropic gas dynamics, nonlinear elasticity, and chromatography.
منابع مشابه
Accurate numerical schemes for approximating initial-boundary value problems for systems of conservation laws
Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating conservation laws do not take into account this fact and converge to solutions that are not necessarily physically relevant. We design numerical schemes that ...
متن کاملBoundary Layers in Weak Solutions to Hyperbolic Conservation Laws
This paper studies the boundary layers that generally arise in approximations of the entropy discontinuous solutions to the initial-boundary value problem associated with a nonlinear hyperbolic system of conservation laws. We consider the vanishing viscosity method and several nite di erence schemes (Lax-Friedrichs type schemes, Godunov scheme). Assuming solely uniform L1 bounds and for entropy...
متن کاملBoundary Layers in Weak Solutionstohyperbolic Conservation
This paper studies the boundary layers that generally arise in approximations of the entropy discontinuous solutions to the initial-boundary value problem associated with a nonlinear hyperbolic system of conservation laws. We consider the vanishing viscosity method and several nite diierence schemes (Lax-Friedrichs type schemes, Godunov scheme). Assuming solely uniform L 1 bounds and for entrop...
متن کاملA Note on Adjoint Error Estimation for One–Dimensional Stationary Conservation Laws with Shocks
We consider one-dimensional steady-state conservation laws with discontinuous solutions. Giles and Pierce [7] realized that a shock leads to a new term in the adjoint error representation for target functionals. This term disappears if and only if the adjoint solution satisfies an internal boundary condition. Curiously, most computer codes implementing adjoint error estimation ignore the new te...
متن کاملVanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data
We are concerned with spherically symmetric solutions of the Euler equations for multidimensional compressible fluids, which are motivated by many important physical situations. Various evidences indicate that spherically symmetric solutions to the compressible Euler equations may blow up near the origin at certain time under some circumstance. The central feature is the strengthening of waves ...
متن کامل