Weighted Energy-dissipation Functionals for Gradient Flows
نویسنده
چکیده
We investigate a global-in-time variational approach to abstract evolution by means of the weighted energy-dissipation functionals proposed by Mielke & Ortiz [MO08]. In particular, we focus on gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow. Sharp convergence rates are provided and the convergence analysis is combined with time-discretization. Applications of the theory to various classes of parabolic PDE problems are presented. In particular, we focus on two examples of microstructure evolution from [CO08].
منابع مشابه
Homogenization of Cahn – Hilliard - type equations via evolutionary Γ - convergence
In this paper we discuss two approaches to evolutionary Γ-convergence of gradient systems in Hilbert spaces. The formulation of the gradient system is based on two functionals, namely the energy functional and the dissipation potential, which allows us to employ Γ-convergence methods. In the first approach we consider families of uniformly convex energy functionals such that the limit passage o...
متن کاملStatistical Estimates for Channel Flows Driven by a Pressure Gradient
Abstract. We present rigorous estimates for some physical quantities related to turbulent and non-turbulent channel flows driven by a uniform pressure gradient. Such results are based on the concept of stationary statistical solution, which is related to the notion of ensemble average for flows in statistical equilibrium. We provide a lower bound estimate for the mean skin friction coefficient ...
متن کاملEffects of End Sill and Step Slope on Stepped Spillway Energy Dissipation
In this study, experimental procedure and laboratory works have been conducted to investigate the energy loss rate on stepped spillway, using inclined steps together with end sill. To have a more elucidated investigation inclined steps with different slopes (Horizontal , 7, 10, and 12 degrees with respect to the horizon) and end sill with different thicknesses (5 and 10 mm) and heights (6, 8, 1...
متن کاملThe spatial relationships between dissipation and production rates and vortical structures in turbulent boundary and mixing layers
A novel approach for studying the spatial relationship between the production and dissipation rates of turbulent kinetic energy and vortical structures is presented. Two turbulent flows were investigated: the zero pressure gradient boundary layer and the two-stream mixing layer. In both flows, a multisensor hot-wire probe was used to measure the velocity components in all three coordinate direc...
متن کاملAn Approach to Nonlinear Viscoelasticity via Metric Gradient Flows
We formulate quasistatic nonlinear finite-strain viscoelasticity of rate type as a gradient system. Our focus is on nonlinear dissipation functionals and distances that are related to metrics on weak diffeomorphisms and that ensure time-dependent frame indifference of the viscoelastic stress. In the multidimensional case we discuss which dissipation distances allow for the solution of the timei...
متن کامل