Continuous dependence estimate for a degenerate parabolic-hyperbolic equation with Levy noise

In this article, we are concerned with a multidimensional degenerate parabolic-hyperbolic equation driven by Levy processes. Using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an explicit continuous dependence estimate on the nonlinearities of the entropy solutions under the assumption that Levy noise depends only on the solution. This result is used to show the error estimate for the stochastic vanishing viscosity method. In addition, we establish fractional BV estimate for vanishing viscosity approximations in case the noise coefficients depend on both the solution and spatial variable.Comment: 31 Pages. arXiv admin note: text overlap with arXiv:1502.0249

Stress relaxation of glass using a parallel plate viscometer

Currently, grinding and polishing is the traditional method for manufacturing optical glass lenses. However, for a few years now, precision glass molding has gained importance for its flexibility in manufacturing aspheric lenses. With this new method, glass viscoelasticity and more specifically stress relaxation are important phenomena in the glass transition region to control the molding process and to predict the final lens shape. The goal of this research is to extract stress relaxation parameters in shear of Pyrex¨ glass by using a Parallel Plate Viscometer (PPV). The PPV machine was originally created to measure the viscosity of glass solid cylinders by compression. It is used in this study for creep-recovery tests of glass samples. With this study we want to know if we are able to measure stress relaxation of glass using a helical spring geometry since it presents pure shear stress, for a temperature near the glass transition region (i.e., 570¡C). The results obtain with the PPV are post-processed using a finite term Prony series of a Generalized Maxwell model. The additional goals of this study are to compare the results with those obtained by a previous student using a tensile creep apparatus, and to compare the experimental results with a numerical simulation using the finite element analysis software Abaqus

Sur des problèmes d\u27asservissements stratigraphiques

On expose les difficultés d'ordre mathématique que posent des modèles récents de sédimentation-érosion de bassins élaborés par l'Institut Français du Pétrole et fondés sur la prise en compte de diverses contraintes d'unilatéralité. On présente quelques résultats partiels théoriques et des directions de recherche pour la résolution d'un problème inverse posé par l'étude stratigraphique d'une colonne monolithologique

PORGY: a Visual Analytics Platform for System Modelling and Analysis Based on Graph Rewriting

PORGY is a visual environment for rule-based modelling based on port graphs and port graph rewrite rules whose application is steered by rewriting strategies. The focus of this demonstration is the visual and interactive features offered by PORGY, which facilitate an exploratory approach to model, simu- late and analyse different ways of applying the rules while recording the model evolution, as well as tracking and plotting system parameters

A degenerate parabolic-hyperbolic Cauchy problem with a stochastic force

International audienceIn this paper we are interested in the Cauchy problem for a nonlinear degenerate parabolic-hyperbolic problem with multiplicative stochastic forcing. Using an adapted entropy formulation a result of existence and uniqueness of a solution is proved