Global weak solutions of a strictly hyperbolic system of balance laws in one-space dimension were constructed (cf. Christoforou [C]) via the vanishing viscosity method under the assumption that the source term g is dissipative. In this article, we establish sharp estimates on the uniformly Lipschitz semigroup P generated by the vanishing viscosity limit in the general case which includes also n...

We combine a sequence of contractive mappings {fn} and propose a generalized viscosity approximation method. One side, we consider a nonexpansive mapping S with the nonempty fixed point set defined on a nonempty closed convex subset C of a real Hilbert space H and design a new iterative method to approximate some fixed point of S, which is also a unique solution of the variational inequality. O...

We study high order convergence of vanishing viscosity approximation to scalar hyperbolic conservation laws in one space dimension. We prove that, under suitable assumptions, in the region where the solution is smooth, the viscous solution admits an expansion in powers of the viscosity parameter ε. This allows an extrapolation procedure that yields high order approximation to the non-viscous li...

Recently, Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl., 2006, doi: 10.1016/j.jmaa.2006.08.036] suggested and analyzed an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set ...

We study the behavior of spectral viscosity approximations to nonlinear scalar conservation laws. We show how the spectral viscosity method compromises between the total-variation bounded viscosity approximations { which are restricted to rst-order accuracy, and the spectrally accurate { yet unstable, Fourier method. In particular, we prove that the spectral viscosity method is L 1-stable and h...

In this paper we propose and studied a new composite iterative scheme with certain control con-ditions for viscosity approximation for a zero of accretive operator and xed points problems in areflexive Banach space with weakly continuous duality mapping. Strong convergence of the sequencefxng dened by the new introduced iterative sequence is proved. The main results improve andcomplement the co...