Attractors of viscous balance laws: Uniform estimates for the dimension

Attractors of Viscous Balance Laws Dissertation Eingereicht Von Jj Org Hh Arterich

Attraction Rates, Robustness, and Discretization of Attractors

We investigate necessary and sufficient conditions for the convergence of attractors of discrete time dynamical systems induced by numerical one–step approximations of ordinary differential equations (ODEs) to an attractor for the approximated ODE. We show that both the existence of uniform attraction rates (i.e., uniform speed of convergence towards the attractors) and uniform robustness with ...

Relative entropy applied to the stability of viscous shocks up to a translation for scalar conservation laws

We consider inviscid limits to shocks for viscous scalar conservation laws in one space dimension, with strict convex fluxes. We show that we can obtain sharp estimates in L, for a class of large perturbations. Those perturbations can be chosen big enough to destroy the viscous layer. This shows that the fast convergence to the shock does not depend on the fine structure of the viscous layers. ...

Uniform Estimate of Dimension of the Global Attractor for a Semi-discretized Chemotaxis-growth System

We study a finite-element approximation of the chemotaxis-growth system. We establish dimension estimate of global attractors for the approximate systems. Our results show that the estimates are uniform with respect to the discretization parameter and polynomial order with respect to the chemotactic coefficient in the equation.We especially emphasize that, this is just the same order(polynomial...

Short-Time Stability of Scalar Viscous Shocks in the Inviscid Limit by the Relative Entropy Method

We consider inviscid limits to shocks for viscous scalar conservation laws in one space dimension, with strict convex fluxes. We show that we can obtain sharp estimates in L for a class of large perturbations and for any bounded time interval. Those perturbations can be chosen big enough to destroy the viscous layer. This shows that the fast convergence to the shock does not depend on the fine ...