# Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence

@article{Mielke2020ExploringFO, title={Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence}, author={Alexander Mielke and Alberto Montefusco and Mark A. Peletier}, journal={arXiv: Functional Analysis}, year={2020} }

We introduce two new concepts of convergence of gradient systems $(\mathbf Q, \mathcal E_\varepsilon,\mathcal R_\varepsilon)$ to a limiting gradient system $(\mathbf Q, \mathcal E_0,\mathcal R_0)$. These new concepts are called `EDP convergence with tilting' and `contact--EDP convergence with tilting'. Both are based on the Energy-Dissipation-Principle (EDP) formulation of solutions of gradient systems, and can be seen as refinements of the Gamma-convergence for gradient flows first introduced…

## 16 Citations

A gradient system with a wiggly energy and relaxed EDP-convergence

- Computer ScienceESAIM: Control, Optimisation and Calculus of Variations
- 2019

A notion of evolutionary Gamma-convergence is introduced that relates the microscopic energy and the microscopic dissipation potential with their macroscopic limits via Gamma- Convergence.

Gamma-convergence of a gradient-flow structure to a non-gradient-flow structure

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We study the asymptotic behaviour of a gradient system in a regime in which the driving energy becomes singular. For this system gradient-system convergence concepts are ineffective. We characterize…

Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions

- MathematicsSIAM Journal on Mathematical Analysis
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The convergence of the discrete to continuous Fokker-Planck equation is reprove via the method of Evolutionary $\Gamma$-convergence, i.e., it is passed to the limit at the level of the gradient flow structures, generalising the one-dimensional result obtained by Disser and Liero.

Effective diffusion in thin structures via generalized gradient systems and EDP-convergence

- MathematicsDiscrete & Continuous Dynamical Systems - S
- 2021

The notion of Energy-Dissipation-Principle convergence (EDP-convergence) is used to derive effective evolution equations for gradient systems describing diffusion in a structure consisting of several…

Fast Reaction Limits via $$\Gamma $$-Convergence of the Flux Rate Functional

- MathematicsJournal of Dynamics and Differential Equations
- 2021

We study the convergence of a sequence of evolution equations for measures supported on the nodes of a graph. The evolution equations themselves can be interpreted as the forward Kolmogorov equations…

Fast reaction limits via Γ-convergence of the Flux Rate Functional

- Mathematics
- 2020

We study the convergence of a sequence of evolution equations for measures supported on the nodes of a graph. The evolution equations themselves can be interpreted as the forward Kolmogorov equations…

Coarse-graining via EDP-convergence for linear fast-slow reaction systems

- Computer Science
- 2019

The strongest version of convergence in the sense of the Energy-Dissipation Principle (EDP) is obtained, namely EDP-convergence with tilting, which is based on a coarse-grained model of linear reaction systems with slow and fast reactions.

EDP-convergence for nonlinear fast–slow reaction systems with detailed balance

- Computer ScienceNonlinearity
- 2021

It is shown that a limiting or effective gradient structure can be rigorously derived via EDP-convergence, i.e. convergence in the sense of the energy-dissipation principle for gradient flows.

Generalized gradient structures for measure-valued population dynamics and their large-population limit

- Mathematics
- 2022

We consider the forward Kolmogorov equation corresponding to measure-valued processes stemming from a class of interacting particle systems in population dynamics, including variations of the…

Coarse graining of a Fokker–Planck equation with excluded volume effects preserving the gradient flow structure

- Physics
- 2020

The propagation of gradient flow structures from microscopic to macroscopic models is a topic of high current interest. In this paper we discuss this propagation in a model for the diffusion of…

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