Viscosity method for hierarchical variational inequalities and variational inclusions on Hadamard manifolds

This article aims to introduce and analyze the viscosity method for hierarchical variational inequalities involving a ϕ-contraction mapping defined over a common solution set of variational inclusion and fixed points of a nonexpansive mapping on Hadamard manifolds. Several consequences of the composed method and its convergence theorem are presented. The convergence results of this article generalize and extend some existing results from Hilbert/Banach spaces and from Hadamard manifolds. We also present an application to a nonsmooth optimization problem. Finally, we clarify the convergence analysis of the proposed method by some computational numerical experiments in Hadamard manifold.

Vanishing viscosity limit for Riemann solutions to a 2 × 2 hyperbolic system with linear damping

In this paper, we propose a time-dependent viscous system and by using the vanishing viscosity method we show the existence of solutions for the Riemann problem to a particular 2 × 2 system of conservation laws with linear damping.

Rheological Characterization of Yield-Stress Fluids with Brookfield Viscometer

This paper analyzes various techniques to use viscometers equipped with vane spindles to characterize rheological properties of yield stress fluids. Specifically, application of Brookfield viscometers to this end is discussed. A wide selection of toothpastes and lotions were tested. It is shown that a simple method based on apparent shear rate and stress, commonly referred to as a representative viscosity method, works well for moderately non-Newtonian samples but may significantly underestimate viscosity for samples with a more pronounced yield stress behavior. To get more accurate data an integral equation relating torque to angular velocity needs to be solved which can be easily done numerically to get a good agreement between the data collected on an inexpensive viscometer and the data from high-end rheometers.

Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping

In this paper, we investigate the global existence and large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Possion equations with time and spacedependent damping in a bounded interval. Firstly, we prove the existence of entropy solutions through vanishing viscosity method and compensated compactness framework. Based on the uniform estimates of density, we then prove the entropy solutions converge to the corresponding unique stationary solution exponentially with time. We generalize the existing results to the variable coefficient damping case.